OK so you've got room to tighten up properly.....so that's not he issue......a 272 carb is not going to do it either.....though it will bolt up fine, Jonsered has the high idle operated by and built into the choke linkage...the husky does not...the high idle is in the trigger handle on the throttle linkage so the best carb for this setup would be from a 670...
On the lower bolt...if you don't have a ball end allen wrench,, cut 3/8-1/2" off the short leg of a regular allen wrench and you'll be able to reach right in there.
However your carb should run it fine though perhaps not with optimum power output....so.....the carb has been rebuilt with a new kit and the 625 ran fine on it...yes?.....you've replaced the crank seals and oil pump housing o-ring...yes?...cyl base gasket new ..yes?... did you put the cyl base gasket in dry or use a sealent?
Why was the choke lever to short????