Not to sound rudd, but every Tecumseh I've ever owned had carb issues. I recently purchased a sears DR clone string trimmer. It came with a came with a Tecumseh that had starting issues just like you described. Had to run it with choke, if I could get it to run. Cleaned carb, no luck. I found a cast iron flywheel for an old 3.5 briggs and pitched the Tecumseh.
I have battled with my last Tecumseh carb.
Perhaps there is a reason Tecumseh went out of business.
I wish you well, good luck. George