No reply from the phone's vendor yet, and I hope to be travelling to Thailand in a couple of weeks, so I'm banking on a new Thai SIM card doing the job. Thanks for your reply. Maybe I'll get on to Samsung's help line in the meantime.
Somehow I've got logged in to the forum as a name that I'd forgotten about. Anyway, just got a new Thai SIM card today, put it in slot #2, and all is working well. The only odd thing is, when I go into SIM Card Manager it reports that its number is unknown, but it shows the correct network, and it makes calls and receives texts okay.
I believe that is normal. My current phone was purchased in Ecuador, and whenever I insert a SIMcard from Bolivia, Colombia, or Perú, they're reported as "unknown number". They all work ok, though, with proper call and data connectivity.