Thanks for the suggestion! As it happens, one of my more technically-minded cousins turned up and called CHT on my behalf, and they suggested we try the SIM card in a different phone, which makes sense. That hadn't occurred to me earlier because we know mom's Verizon iPhone is locked, but the SIM card worked fine in my cousin's phone.

I called Sprint again and they swore my G3 was as unlocked as they can make it. So either there's some setting I'm still missing, or it's something about this particular phone.

My cousin did find a workaround though -- mom has a throwaway phone she got on her last trip here as an emergency backup. It apparently is some flavor of prepaid voice only. But we swapped in my new SIM card and turned on wifi tethering, so now I have to carry both phones but that's totally acceptable for my purposes ^