There are way too many variables in play to get a boost pressure estimate over the internet, notwithstanding the details you have provided.
If available, your best bet is to reference a turbocharged 300 CI engine build with as much similarity as possible to your general concept, and use that as a starting point.
If unsuccessful in finding such info, you will have to develop your application by trial and error.
7.8:1 seems like a pretty conservative build. I suggest you proceed with that and then gradually explore the knock limited performance. As you know, you have three main knobs to tune with, i.e. boost pressure, spark timing, and fuel enrichment; and a fourth, as an ace up your sleeve, fuel octane. You can trade off all 4 of these variables as you wish.
If you employ intercooling, that will make a bigger difference in knock limited performance at given boost pressure than anything you can do with spark timing and enrichment and no intercooling.
A further design element that shouldn't be overlooked is the camshaft.
I have no clue what factory or aftermarket camshafts look like for this engine, but you want one with limited overlap. If you can provide details or links to the factory or aftermarket camshaft offerings you are considering, I can give you my assessment of each one and my rationale. If a custom grind is an option, then it gets interesting, and deep.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

Thanks for the response. I have followed abut a dozen internet builds with these motors. The biggest issue is no one gives feed back after they are running. Based off of what I have seen, I should be ok up to about 10 psi.

What I was hoping to look at was the heat produced by compressing the air (to 173psi), and how much less heat is produced by lowering the compression (to 150psi). I could then take those numbers a use the new intake temp and pressure to see where I am at.

The DCR and PSI number I gave reflects the cams being used.

The sock cam is 268/192 268/192, 110LSA, set 4 degrees retard and .37" total valve lift

The custom cam I would get would be 270/203 270/203, 114LSA, set 0-4 degrees advanced, total lift would be .44"

Both cams look reasonable. The custom grind will be a nice upgrade if you have fuel, intake and exhaust mods to take advantage, not to mention the turbo.
Is an intercooler an option? That is always the biggest bang for the buck with any boosted engine. Be advised that the increased air mass flow due to the intercooler normally requires a larger compressor stage on your turbo, unless it is oversized in the first place.
I wouldn't get too wrapped up in DCR or trying to calculate charge temperature. Just build your base engine conservatively, and see where tuning takes you. The only thing to keep an eye on, especially without intercooling, is where on the compressor map you will be running. Compressor efficiency can and will have a huge direct effect on charge temperature, and indirectly, exhaust backpressure, which is also a driver for detonation.
If forged pistons are an option, I strongly recommend them. The other weak link on most engine designs not originally intended for boost is the head gasket seal. Just identify and use the best practices for your engine. Depending on the base engine design, other weak links can be exhaust valves, bearings, and connecting rods. If these are known failure points when adding boost to the 300 CI, I recommend looking for upgrades.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

Inter cooling is part of the plan but I’m not positive what size I can fit. For now I’m estimating 40% efficiency.

As far as internal motor parts go, I would like to stay as close to the original design intentions as possible or things get expensive fast and/or reliability goes to crap.

There are good head gaskets available which I will use and arp heads studs.

The rods will handle 300 lb/tq forever and under the worst conditions, so I think it will hold to 500 lb/tq under decent conditions. At 4,600 rpm the rods are 2.6 times under their failure limit. I will not be pushing the 4,600 mark.

There are no off the shelf forged piston options. The best piston available for my application is this hypereutectic.
https://www.summitracing.com/parts/uem-3118h-030/m...

To go forged would involve a custom set from auto tech for about $600. My biggest concern with forged is risk of cold seizure. If I can eliminate that I will.

The fuel/spark system will be sequential multi port injection driven by the Holley HP coupled to the stock TFI distributor. Simple and easy. So knock sensing will be monitored closely... do you still think forged pistons are necessary?

Hi Wesman,

I don't know how to answer your OP question, but I think I can give some rough guidance. If I assume a polytropic exponent for the piston engine compression cycle that is based on empirical thermal leakage data (but does not include leakage past the rings), I can estimate a peak compression pressure at various CR and MAP.

So the details of temperature get a bit involved, and depend on the fuel/air mixture ratio, the possible use of an anti-detonant injection, and the intercooling hot side effectiveness (if applicable), so don't read too much into the PCP graph. But, if you can run detonation free with 10:1 CR and 1 bar MAP, and if you can control the temperature rise to about the same value for the reactive gases just prior to TDC, then you should be able to run the same detonation tendency at 5:1 CR and about 3 bar MAP. (And yes, I agree that pressure does not directly effect detonation tendency.)

In any case, you may have fun with the attached graph. Just to add some real world value to the graph, I was involved in a Reno Air race engine that was running about 3.5 bar MAP with a CR of about 5.5:1. We ran 100% power for about 30 minutes, and obviously detonation free (as the engine wouldn't last 30 seconds if we encountered detonation). We did NOT intercool because we did not want the drag penalty. But we did provide plenty of 50/50 methanol water fluid used as a anti-detonation injection (ADI). The ADI was injected just downstream of the turbocharger and tuned to provide a 60 C (140 F) intake manifold temperature).

See attached excel file for interest.

• https://files.engineering.com/getfile.aspx?folder=58e19d75-9a6c-418b-b123-1

Trail and error is a deal for very rich people. When you do not know, you do not do it if you do not was to do it again. First, I have found that no one every wants to go slower. They have never ever called me back to ask me if I can make it go slower, its always pushing it to the extrem-er! I did an engine 2 years ago and done all the math with everything I have learned in 40 years of engine building and told him to keep this engine at a 300 hp shot of NOS with my tune up only. He ran the engine for about 3 months and finally go beat. So he calls me and ask me if we could put 400 on the engine. I said sure but when it breaks it will break badly. I gave him my best tune up and hoped the head gaskets, pins, rings and tuner he used was dead on. It ran beautiful and once again he was on top. Now we have several months and guess what, he called me ask now asked me for a 500hp tune. I told him now its gonna be a margin of error area of a fraction figuring cylinder pressures, rpm, heat, fuel, dynamic workings of the whole engine to get from point a to b. I advised him with a big NO. He still wanted my tune. I gave it to him and said, "when it comes apart it will be ugly" Well he called me back that Monday and told me the little 434ci SBC Dart Block Billet Crank, forged Wiseco NOS pistons, tool steel pins and every thing else I shoved in this with EAGLE steel rods went 5.06 in the 1/8 and he won. Now he has his mind set nothing will break the engine. It did stay together and the point is never put it on the edge if you do not have to.

He has never pushed it any further because I know where I put it and I always leave room for growth. Men can never go fast enough. So my answer to you is that I would use 4:1 compression with a custom piston and your tune up will be so safe you will have plenty of time for growth. A little extra spent right now on custom pistons for your application will allow you to run 30 PSI of boost with pump gas if you want to. We have done this a few times and people always do the same thing, they call and say wow!. Now, you do have to build the bottom end, with rings, connecting rods, crankshaft to handle the power, or it will just break. So if your engine parts are marginal, you can still run the 4 or 5:1 or even 6:1 compression and be as safe as you want with 15-20lbs of boost and your margin of error can be tuned by Ray Charles. It will not be as sensitive to extreme pressures which allow you to be a yard stick off and it will not hurt it. Just read your spark plugs and use common sense. I have found E85 requires no inter cooling needed at all and it is readily available at the pump in most places. Your engine will stay super cool with minimal cooling items, no special fans, nothing but a water pump, stock fan shroud, fan and a good set of belts. I would tell you something but I think people will not understand the principal so if you want to private message me I might hint it to you if you would like, hope this helps a little