An NFL stadium, built in the early 1970's, where I was in charge of the trades had such tamper resistant stops. The plumbers would use 4-way hose bibb keys. Maybe this will be a fit for yours. They also make (or used to make) friction-fit keys. These were tapered to fit damaged stems.
Maybe this will work for you, but if the stem snaps, you may need to replace the valve:
It's how I freed many, many gate & globe valves on my plumbing & hydronic system when I bought the house:
Turn off the branch supplying the valve, remove the packing nut, wrap electrical tape around the jaws of water pump pliers (AKA Channelocks) and try to turn the stem. Maybe give a gentle counterclockwise turn first to break corrosion. (The tape is to try to prevent putting marks on the stem that might cause packing leaks.)
Last Ditch Effort:
Will the stem and nut from a current model angle stop fit? Most of those in my house accepted Brass Craft or Mueller stems.
Take the packing nut off and grab the stem firmly with water pump pliers or gas pliers. You'll damage it, so be ready to swap valve bodies if this fails.
Hope this helps.
Also note that I'm not currently a plumber, so maybe ask the real plumbers here if these are bad ideas before proceeding. (Completed my apprenticeship in the 70's and worked almost exclusively pipe fitting & DWV installations, thus I've very little knowledge of faucets, drains & such. When PVC became the norm, I had to stop because of anaphylactic reactions to the solvents.)