. I think I will need to drill/grind out the rivets to give the sliding arm enough room to move. The next step could be to tap the hole and put in a short machine screw that will not go too far through the hole.
Imho, this is probably not worth doing, if I correctly understand your proposal?
1. The thin wall section won't allow many threads to be cut (the connection will therefore be weak), and they will be very corrosion prone. They won't last. Hence you commonly see nuts welded onto thin box section material. At least you can grease these...
2. The chassis itself, being dip galvanised, will not be improved by cutting/drilling.
"Galvafroid paint" and similar may help, but like many Engineers/maintenance materials it does not seem to be as good as it once was (perhaps a little like me?). It is also now very expensive. It cannot protect threads.
I contemplated drilling through and using lynch pins or similar...but see 2 above.
In the end, on the odd necessary occasions, I removed the bent-bar clamping /pinching handles and replaced them with stainless bolts, long enough to have a free nut on the bolt stem. Well greased as they run in "galv" threads.
This allows the board rail to be pinched with the bolt, then locked off by backing down the free nut on to the captive nut on the chassis. However, you will then need to carry a shifter, no hardship for Engineers
GWs solution is far better!