Burping was done on a really good incline, but not for hours (20 mins max), so it could be a possibility to try again.
I'm working on the theory that it's not the heater core - mainly on the basis that I can't face taking the whole dashboard out. Naive? Perhaps.
Got another working theory, suggested in a thread over on
http://toyotaownersclub.com/
Could be worn out solder joints on the heater control panel.
Took it out this evening, and re-soldered all the joints (some of them were looking a bit sad).
Put it back in, and heating was working ok, at least for the short time I tried it.
That proves nothing yet though - I need to take it out for a longer run tomorrow.
If not working ,then I'll try a longer burp (excuse me!), and also look at this air mix control servo, as I still think that's a possibility.
If still no joy, then yes, I'll have to really consider the heater core itself.