I did my hydro-static testing many years ago on (shorter) nuclear power plant piping, where temperature changes (while the pipes and reactor vessels were filled solid) were mostly from running pumps or heaters, not from environmental temperature changes.
But similar rules will apply, particularly since your pipe is so long.
Note: Find out WHY the ten gallon rule is imposed: I suspect that it comes from some "authorized" leakage value for the actual fluid. The person/regulator who wrote that spec wants to assure himself/herself/her congresscritter that no leaks have occurred where they can't be seen, and that no leaks are being disguised by the hydro pump. But if 10 gallons won't pressure the pipe - even assuming it can be completely 100% vented and the water and pipe and fill are at a steady state temperaure! - then you'll never pass the test.
1) Calculate as close as possible (including elbows, fittings and valves!) the INTERNAL volume of your entire pipe run. You may find that the 10 gallon rule is impposible to meet if the pipe run is long enough.
2) To calc the volume needed to raise pressure in the entire pressurized run, assume you could fill the pipes and all branches 100% full at a static temperature to NOP (normal 100% operating pressure.)
Then, to raise pressure 1% PAST the completely full/static temperature point/completely pressurized point, the added volume of water will have to do two things: compress the water, AND expand the pipe walls (because the added stress inside the pipes). It is these two EXTRA volumes you need to calculate and compare to the arbitrary 10 gallon limit.
In other words, going from 300 psig in a completely full pipe (perfectly non-expanding) pipe using perfect (non-compressible) water to 330 psig in a real pipe filled with real water will require three volumes of water:
Vol1 = amount to raise pressure 30 psig,
Vol2 = amount to fill the expanded volume of the pipe as the pressure expanded the pipe, and
Vol3 = amount to make up for the small compressibility of the water.
Obviously, a 30 psig increase is so small that it is almost neglible, but your real hydro pressures are much higher.
NOTE: 8 US gallons = 1.0696 ft^3.
200 ft of sch 40 10" pipe is 109.46 ft^3
200 ft of sch 40 20" pipe is 385.92 ft^3
so your 10 gallons is only a small fraction of even a short pipe run.
It won't take long for your 1.0696 ft^3 of "allowed water" to become useless in raising pressure.
Try this, once you have calc'ed the actual volume needed under iso-thermal conditions.
Remove all bellows and pumps, in-line eqpt that is pressure-sensitive (we were NEVER allowed to hydro-test bellows!) and insert blank flanges and flanged spool pieces in their stead. Check for check valves and locations of your primary secondary, and backup pressure gages and relief pipes. You DON'T want the increase in temperature during the test to overpressurize the pipe! You DON'T want a branch to be isolated and over-pressurized because a check valve closed tightly and "isolated" the branch as temperature rises.
Fill the pipe completely, vent it, and leave it attached to a standpipe/expansion tank for two days to equalize temperature. Watch the standpipe level through one full day to see the effect of daytime temperature on volume as temperature raises in sunlight. Then start your hydro test.
Try to measure your expected temperature change now. It might really screw up your work despite your best efforts at venting and filling.
As always, check my work. Check my assumptions.