My Ford truck went from an easy to start state to a stubborn start after I rebuilt the carb. The problem turned out to be the new power valve was dripping gasoline into the intake manifold when the engine was off. So I’m with you on the leaking fuel component floods the engine idea being a likely cause of cranks ok but hard to start. After I replaced the defective power valve, it returned to r-pop-run … i.e. now with the power valve problem fixed it doesn’t even get to the second r in rrrrrr before it pops & starts up, purring & ready to go … lol …
Good for you, it sounds like you’ve solved the leaky injector problem and have a consistent fuel pressure. 34 psi seems maybe a little low though for a Honda, maybe double check that to make certain. A lower fuel pressure could certainly cause poor running, but I’d guess 34 psi would still be within the range where the computer could compensate for it once the engine warmed up and the O2 sensors came on-line. You might see a significant fuel trim though. If you have the capability, check to see what the fuel trim values are maybe.
You compression values seem ok, doubt that’s the problem. hmm … I’d guess either the ignition timing is running amok, or there’s still a problem with the spark. Double check the ignition timing with a timing light at idle. If that’s ok, replace the distributor cap and rotor. Still a no go? Replace the ignition module is probably next. Either that or find a shop who has the Toyota scan tool, lab o’scope, and other necessary equipment to properly diagnose this problem for you.
BTW, wayward valve timing could cause this. I doubt that’s the problem b/c your compression values look ok, but its possible to have ok compression with wayward valve timing. My Corolla has a timing belt so if I’m concerned about valve timing I can remove the upper timing cover to expose the cam sprocket and check the valve timing with a timing light. Not sure of your engine configuration whether this same method is possible for you though.