You say it revs up fine in neutral and revs up fine when you put hydraulic load against it right?

Try pulling the flex plate bolts, back the converter away from the flywheel it's just a few bolts, start it up put it in gear and see if it revs up.

This will eliminate anything mechanical really quick. A bad converter will bog an engine down in gear. If it doesnt change you've only spent a few minutes and then you can concentrate your diagnostics to possible "electrical" or other issues as you first thought. If deadheading the hydraulics in neutral doesnt bog the engine down it sound like you could eliminate fuel issues too. Most oil pressure safety systems will shut the engine down shortly after not sensing proper oil perssure so I dont think thats it either.