I'm far from an expert on this, but I don't think the "rifle only"/ high velocity ammo has been made since the '60s or maybe early '70s. I believe this was loaded by both Winchester and Remington with an 80 grain bullet and had a muzzle velocity of a little over 2,000 fps.
I don't know about your REM UMC ammo; that's pretty old. There are many here who know much more about this than I do and perhaps they will give you better information. I've loaded for the .32-20 for years and have fired some factory ammo. All of it, from Winchester and Remington, had 100 grain bullets and only chronographed around 1100-1200 fps from rifles.
If I had a strong .32-20 rifle (Winchester 92, Winchester 1885, or modern Marlin) in good, tight condition, I'd fire a few rounds of your ammo and chronograph it. Good luck-