Before doing anything, have you nailed down exactly what the source of the peeling paint is? Is this condensation caused? If the source of the problem is not addressed, the paneling could have similar or worse issues.
Understand the logic of this advice. Both the Contractor and us agree at least that the old paint and primer is the culprit, the Contractor is not willing to say that the Sub-Contracted Painter should have stripped the old Paint and Primer first, before applying a new coat, which is our position.
That being said, there is agreement that it is not a mold issue, or something like that. We both agree that there is enough adequate ventilation to the attic space above that portion of the house.
That being the case, that we have some level of agreement, the Contractor has agreed to provide the "Labor" at no cost to us, in good faith; and we, in turn, agreed to absorb the cost of the materials.
Care was taken today, to ensure that the Paneling and adhesive chosen (and the Faux Beam material too, for that matter, are made of the kind of materials that will not react adversely to temps and dryness as would be typical with a wood stove application.
-Soupy1957