Another thing to consider is whether your heater is ingesting water when washed or in rain. This can happen when the drains for the plenum chamber block and the plenum floods into the heater assembly. Easy to check for by lifting the plastic panel over the plenum (under the wipers) and checking visually and with a gentle water flush. Expect to find 2 drains in there - one may be obscured by the fuse box, but you can feed a wire or stick past to give it a stir.

May be a long shot, but cheaper than a new heater core.

Wolfgang