It is not broken just popped off, as you can see in the 2nd photo the arm does pop right back on.

Besides the obvious solution of welding, which I don't wanna pay someone to do, will 30-minute epoxy or JB Weld epoxy be strong and heat resistant enough for a permanent fix?

G'day Mate,
I would take the throttle part off the throttle barrel, It's usually held on with a small "allen screw", support it on a vice or table, slip the throttle arm back on, & peen the riveted sections, with a small punch.
Do it carefully, & it will be better than new.

I had exactly that problem with a Kangke SK.50 engine. The arm was held on with four little pressed/swaged dots. I had to fly at 3/4 throttle until the fuel ran out.

JB Weld did fix it, but eventually I swapped the carb for a Perry anyway and never looked back.

I had the same thing happen with an OS 70FS, as Alan mentioned, you can remove it then peen it back on but JB Weld after that is a good idea. I just bought a new one for a couple bucks at my LHS. That doesn't happen often but it happens enough for my LHS to stock them.