You could try these from McMaster Carr.
https://www.mcmaster.com/#catalog/124/3363/=1cbq0bg
Threaded tubes.
Get the right length. Long enough.
Cut to fit between plates and screw in from both sides.
Make sure there are enough threads left at end for screw when you cut.
Some tubes have threads all the way through.
Stainless steel would be good. 8-32 threads.
2 stainless 8-32 pan head screws for the ends.
I think 1/4" OD tube is the smallest they have.
Yours looks like 3/16".
I think 1/4" would work fine.
Link did not work. Look for these.
Threaded Standoffs, Caps & Pillar Posts
Female Threaded Round Standoffs
Fully Threaded
Partially Threaded
Use standoffs to position components in assemblies, as well as to separate or connect parts.
18-8 stainless steel standoffs have good corrosion resistance and may be mildly magnetic.
Zinc-plated steel standoffs provide some corrosion resistance.
Aluminum standoffs are lightweight, nonmagnetic, and mildly corrosion resistant. Material can vary between 6061 and 2011 aluminum.
Zinc-plated brass standoffs are electrically conductive, nonmagnetic, and have a corrosion-resistant finish.
Nylon standoffs have excellent wear and abrasion resistance and also offer resistance to chemicals and solvents (except mineral acids). Exposure to moisture may cause them to expand.
OR, just get a piece of stainless tubing and a screw long enough to go all the way through tube to the threads on the butt plate.
Good luck.