Is a 15-month-old TM30 receipt still valid if I haven't changed my address?

If you havent changed address or filed a subsequent TM30 then you can still use it

That depends on the province you're staying. Some do require a new report anytime you are back from another province, some other just require a new report when you are back from abroad. Some other (eg Samut Prakan) don't even require a new report at all if you haven't changed your residence address (ie you come back from abroad, just walk to IO with the old TM30 slip and they will just put a confirmation stamp).

Better ask your local IO first.

If you haven't stayed at any other address outside of the province you're in, it's fine. There's no expiry date