Trying to tune up the mechanical FD (Shimano 2203 triple) on my old road bike. I followed the park tool guide and I seem to be stuck.

The problem is that I can't find a setting that would result in correct shifting from the middle ring into the big ring. Depending on the position of the high limit screw, I see two outcomes: either the chain does not get off the middle ring at all, or, if I turn the screw even a little bit, the chain goes right over the big ring and falls off the outside. There is no middle ground. I get the feeling that the derailleur cage is too wide to shift correctly. Chain tension does not seem to matter and vertical position of the FD is set correctly.

I suspect that my problems are caused by mismatched components. The bike originally had this 2203 triple FD, a 8-speed chain and a 8-speed crankset. I had most of the drivetrain upgraded to 10 speed piece by piece. It used to work more or less correctly, though shifting into the big ring was always less than 100% reliable. Right now I'm trying to put the original 8-speed crankset back on and that's where things are going sideways. Visually, it looks like the 8-speed crankset (Bontrager) has slightly narrower spacings between chainrings than the previous "upgraded" one (105). I guess that could explain the troubles (this crank and this FD used to work properly with a wider, 8-speed chain, but not with the narrower 10-speed chain.) But I can't find any confirmation online that different road triple cranksets can have different spacings.

Is there anything I might be missing? If nothing else works, I'm thinking to get a new 10-speed specific FD, but I'd rather not spend any money.