Okay, I'll be the first to get this over with. You Do know how to drive stick, right?
Alright, that's over with. Having to lean on the shifter does not sound good at all. I know the old trick of when it's difficult to get the shift in you give it a little gas. But you sound like you are a little more involved. My vote is to go to two to three tranny places. Get a free inspection and see what everyone says. And don't feel bad about getting a free inspection and then going "Thanks, bye now. I'll be back."
Do you have any friends who are experienced manual drivers? Let em' take it for a spin and see what they say.
Good luck.