Hard to give a definitive cause for the motorboating on the Mesa, for in theory it would suggest components in the path of a valve cathode changing value over time, allowing the amp to 'runaway' . A tech would have to explore that one in person.
On the Classic 30 I would :
1) Clean the valve pins and sockets with 'Servisol' which you can get from Maplin - or some WD40 used sparingly. This should clean out any problems brought on by oxidisation of the surfaces causing intermittent contact. gently wiggle each valve in it's holder, but not enough to loosen the grip of any individual pin holder - just enough to work the fluid in between the pin surface and pin holder surface.
2) Very gently tap the side each pre -amp valve with a pencil, to see if any one is more microphonic than the rest.
You have already said that you are willing to re - valve but first let's assume that the problem has occurred due to the condition the amp was stored in, therefore clean ( as at point '1' above) - and if you can reach in safely, spray your control pots with the Servisol too and give them a few turns back and forth to work it in.
I hope that starts the ball rolling.