Any question answered...

I'd give the shim a go. If it works, you could glue it in place (inside the bar), thus causing less fiddlage at the track.

Double sided tape for shim attachment: less mess, no drying time, predictable thickness, easily removed with readily available solvents should the need arise. Works well enough mixing & matching 'classic' (i.e. not original and sometimes worn) motorcycle components.