As motioned before a cal .22 will do the trick a cal 12 or 16 wil damage your stuf, btw a cal 22 will fly to your next door neighbours.
A pallet gun? and some patience? you must shoot a lot of them.... but they will come back...perfect as roast a pigeon, bbq, stew, boiled, backed can be, after one full year you want something else...
You cannot win.
Pigeons and other birds even mammals (fox marters ferrets ect)will swallow small stones to help to grind up food in there stomage.
Make sure all is fixed by a glue, then they won't pick them up, and lose intres.
Sometimes they are mistaking the small stones for a snail or something, seagulls even drop golfbal size stones in the hope that there is a jummy tread in it.
Oke tackel a other problem.
Also food related:
Make sure your tracks and at least 50cm either way of your track is plant free, all small plants carry seeds, and that is something they also want to have: seeds and young plants/sprouts.
Get some cats and or dogs, train your dogs to scare away birds.....Oke it will save me some food

but the damage on the track....
Cats are more gentile...
As far for your planning, get yourself some thin pvc or alu sheet 1mm thick.
Make yourself some arches like you want, nail or glue the sheet down.
Heck get even 3mm 5mm max plywood and put wood stain on it.
Plywood and foam pvc can be carved like roofing tiles structure.
Or get some 1-2 plexiglass Lexan glass...
If you going to do it, than do it good!
There are some railroads companies that needs protection in the mountains, i really hope someone will shime in on this one. that is all i know, sorry.
I even thought in heavy forest they also had/ or do something like this.
I hope this story will give you some food for thoughts...
With best regards Igor...
Ps some dogs between 40 and 60 .... you dont want them around your track chasing a bird.... really you dont want that......really you dont want...