Sounds like a vacuum leak or broken/stuck reed or timing problem to me. Check all the hoses and make sure the carb nuts are tight. Did you check the reeds when you had the carbs off? Maybe something got sucked in there too... Sometimes you will get a poor idle but run good at high speed if the timing is off (too far retarded), so you may want to check the timing as well. We have a couple Johnny Rude experts on the site here, and I am sure one of them can chime in with some good ideas as well. Good luck!
New plugs but have you pulled them since you installed? If so, what do they look like?Checked all hose connections for air leaks?Carb rebuild done properly (that you know of)?
With that age, have you done a compression test yet? Last one I saw that had those symptoms had a dead cylinder? Just something to check. make sure your throttle is all the way open, all plugs removed, and as stated before see what your new plugs look like after you ran it. good luck
Check the wiring coming out of the timer base and look for breaks. Try to manipulate the wiring while the engine is running using a stick or something not conductive and see if you can change the engines attitude by sweeping the wiring front to back or back to front to mimic rotation of the timer base and see if it runs differently at idle. Understanding this is a pre-mix engine does she smoke excessively at idle? Also do a spark check, all plugs out, normal idle position, look for weak or no spark and then fully advance the throttle, if you have a binnacle control box you can do this with the box pegged in neutral and check spark again, look for a difference between idle spark and pegged spark. This points towards a wire issue in the timer base harness. This makes a lot of assumptions that everything else is right in the setup. The quirk here is that you can choke it restart which points towards a fueling issue but I've seen where choking to restart can mask a base timing issue, so I would make no assumptions just yet that the engine is linked and sync'ed correctly without verifying it. Incorrect float heights can do this also.
100 psi compression is getting low, do you have tstats in motor and is it running at 125-145 degrees? Todays fuels need the heat to burn, you can't remove the tstats anymore. If motor is running at correct temp, pull intake covers and check piston skirts. If they are smooth and the cyl walls have lost their crosshatching then you are not building enough crankcase vacuum/pressure to run the fuel pumps and pull fuel charge from the carbs. Compression test will not show this problem.