I am in the final stage of my build of my 84 Bianchi Special with a completely new modern groupset and came up on a problem... the front derailleur I got was a braze on (I could not find a clamp on at the time) so I purchased a braze on adapter (Shimano braze on adapter which comes in 31.8 mm in size but has 28.6 mm shim to fit the old school frames) which I've installed and it seem fine. I came upon a problem while I was adjusting the derailleurs. When it's in the small chain ring and biggest cog (ideal climbing gear ratio), the chain is rubbing on the inside part of the front derailleur and I can't seem to go in any further. After about an hour of adjusting/messing with the derailleurs, the distance that the derailleurs that needs to move is about the size of the shim. I am thinking the shim is pushing the position of the derailleur further out from the frame and this is causing the front derailleur to touch the chain. Did anyone experienced this problem before? If I changed out the braze on adapter which fits the seat tube size of 28.6 without the shim, would I have enough room for the front derailleur not to rub against the chain?

Often it's the "knuckle" of the derailer link that hits the seat tube when the derailer retracts fully, which then limits how short that the bottom bracket spindle can be in some instances.

I've used sandpaper to make a slight relief to the area of interference, with the grit side of course facing away from the frame tube and with the sandpaper moving against the derailer knuckle, but have also seen derailers fail because of too much metal removed from near to where the spring is seated!

A narrower chain always buys a little extra clearance within the front derailer cage, for what that's worth, so I often use 9sp chain even on older bikes with Asian freewheels with as few as 5 speeds.

Can you identify the exact point of contact that is limiting the front derailer's inward throw or retraction? Sometimes a little bit of grinding with a Dremel can increase inward travel, but again one can cause parts to break if this isn't carefully applied.

If yours is a modern "2-piece" crankset, perhaps the driveside spacing can be increased slightly at the bb spindle or between the bb cup and the frame.

Get a new 28.6 front deraileur that clamps on.

How many speeds is the drivetrain (FD and RD) derailleurs that you are trying to use?

I have a brand new Shimano 105SC FD-1055 7 speed double front derailleur clamp-on 28.6mm the box, and I might be willing to trade you for your braze-on front derailleur and 31.8 adapter clamp. Which front derailleur do you have?