Thanks for the quick responses!
I am the original owner of the bike. I can say confidently that whatever freewheel is on it, it had when it was new. However, I haven't ever tried to remove the freewheel before since there had never been a problem with it before now, so I don't know what type of tool it requires. It has been so long since the bike was put in storage, the chances of me having the old tool are pretty much zero, sadly.

The pointer about friction shifters is very nice to know; I'm glad I should be able to make it work without investing a bunch in buying completely new running gear. So am I to understand that a replacement freewheel would probably be incompatible with the SunTour shifting equipment, then?

BTW, sorry for not providing images.
I'm unsure what would be most helpful, but I hope these are informative