Your question is more complex than you may imagine, as different engine designs, in different condition, with different oil, operating in different environments, can have vastly different oil pressure and temperatures.
I have seen engines that blow the filter canister (that takes at least 150 psi) and others that idle at 3 or 4 psi. In both these cases the figures are estimated as they are off the scale of the gauge.
Temperatures can range from ambient in Alaska to over 150 deg C.
For good healthy running, I aim at about 10 to 15 psi per 1000 RPM, and like to see the temp at at least 90 deg C when hot, and preferably at about 105 to 110 deg C, maybe up to 130 deg C for synthetic oil, but I would consider 130 as marginal. But as I already said, it is really much more complex than this.
Also, for a prestart lube as you describe, you need to do more than just introduce oil to the galleries, as piston, and often cam lobe lubrication, normally comes from oil spray, mainly thrown from the crank. This also depends on camshaft location.
You could set up a spray bar system to the cam, but the pistons and rings, how to get the oil between the piston and the bore for full coverage of skirt and rings with the piston anywhere in the stroke, without anular groves in the bore (read ring breakage and blowby problems) I can't imagine. I hope you have more creative vission than me, as I would like to see a workable system, as cold start greatly increases engine wear at present Regards
pat