Sorry it's been so long, but I have an update. We did the repair that Semperfi8387 shared from the Hull Truth and it seems to be working fine (we added some clear epoxy to the outside of the set screw as well). However, I think we fixed one weak point and that exposed another. The outdrive hydraulics still lose some pressure and the outdrive goes down when under moderate to heavy throttle. I believe the gasket at the bottom of the trim reservoir is now leaking (but only under a heavy load) because I sat on the outdrive (out of the water) while my brother-in-law trimmed it up and down with no major leaks. However, I did notice an ever so slight amount of oil at the bottom of the reservoir (near the gasket) after doing that a couple of times. I suspect that when the engine is throttled up and the hydraulic system is under that strain, just enough oil leaks to allow it to be pushed down rather than hold its position.
I'm ordering a new gasket for the reservoir and will be replacing it as soon as it comes in...