Tube amp fades in and out.

I'd look for a failing cap somewhere.

A slow smooth clean fade out / in usually indicates an intermittent connection to a tube heater.
Mesas can be tricky to work on, so taking it to a competent tech is a good idea.

I was about to suggest checking the tube sockets for loose connections as problem cleared when you replaced tube then eventually returned. 

few different methods but the one I use is say a dental style pick and very carefully close them down slightly by inserting the pick (small pointed tool) between the pin tube and the tube socket and very gently close it. Each pin tube on the socket has a split on one end. I close it just enough that it is no smaller than the smallest diameter pin tube on the same or another socket. In order to keep from spreading a pin tube you need to carefully insert the tube into the socket. When removing a tube just slightly rock the tube while pulling up on it (sort of like pulling a tooth).

Glad you added this about power and decharging caps. I found it discharged well buy turning amp on, connecting guitar and strum it while pulling the power plug (not turning off). Still use a voltmeter to verify.