Your good there, that rules out a worn front cover and/or lube pump.
Another freebie, quick check I forgot about. Pull the top off of the fuel filter housing and check the color of the fuel in it. Should be clear. If it's black, you have a blown oring on the injectors and will have to replace them.... This is another area you could lose oil pressure needed to fire the injectors. May want to get your hands on a 5000 psi gauge and check the actual oil pressure at the rail plugs, you need a minimum of 400 PSI to fire the injectors when cranking.
Explanation of oil loss in the resevoir:
On the 7.3 PSD the HPOP resevoir is fed by the lube pump on the crankshaft and the gearotor rides on the aluminum front cover. If either is worn bad enough the engine will start and then die a few seconds later when the lube pump can't draw a prime fast enough to refill the HPOP resevoir that is feeding that thirsty HPOP leaving you with a truck that will crank and not fire until it gets oil back into the high pressure system either by cranking a long time or pulling the plug and filling the resevoir to prime it.
If this happens you HAVE to pull the engine if you need to replace that $400 - $500 front cover. No getting around it. I'm glad to hear that this isn't your problem.
Early 7.3 PSD engines also had a check valve that would stick allowing the oil to drain back out of the resevoir. I can't remember the date of the change to a standpipe vs a check valve but it was only the first few year models.