Just about 3 weeks ago, I had to get a 11hp honda engine running. The engine had sat unused for 4 or 5 years. It would crank, but wouldnt run under load. Like you I had to use the choke to keep it running. I removed the bowl off the carb and it was full of varnish. Cleaned it up, remove the float and needle, needle was actually stuck. Cleaned it up, put it back together and engine still wouldnt run right. took carb back apart and tried to remove the jet as it was completely clogged. After fiddling with the jet, I was afraid it wasnt going to come out so I took my torch tip cleaner and started running the smallest cleaning drill thru the jet and stepping up in size of drill until I reached the size that would just barely go thru the jet. You dont want to force the cleaning drill thru the jet as this would open up the size of the jet and make the engine run rich all the time. Put carb back together and engine ran fine, but would still bogg under load. Changed sparkplug and then I used it for 3 or 4 days without any problems. Since your engine has been setting for long time, and you are having to fiddle with the choke to keep it running, I think my first step would be to get the engine running right. Clean the carb good and maybe change out the sparkplug. Running with the choke partly closed can foul the plug.
Once you have the engine running right, I would then try diagnosing the hyd's. As NS Maple said, sounds like the relief pressure might be set just a tad high. The relief adjustment should be located on the control valve. Since your valve will retract after pushing the lever and turning it loose, and stop at the start position, the detent pressure should be set pretty close and should not need to be messed with. Since you dont have a pressure gauge on your machine, you can set the relief by ear. You already know that the pressure is set high enough to stall your engine so it should just be a matter of backing out the hex screw under the cap until the engine just boggs, but doesnt stall your engine. You wont know what the pressure is, but it will be at the max that your 9hp honda and pump can produce without stalling.