Had a Marshall 5203 SS Combo that did similar things.  The guy I traded it to, said noise stopped as he was firing it up every day...In both cases the amps had not been powered for a long, but unspecified, length of time.

So the noise this TM 60 was making has mostly stopped: none on boot up; occasional very low level while playing, but thay may have stopped too.  In fact I used on a gig last week.  IS it possible that an electrolytic cap gradually reformed during use?

They quote $80 an hour.  Not sure the additional time for them to connect and disconnect from a chassis (or test rig) at their shop would be less than the shipping.  Shipping charges will likely be based on dimensions anyway, so additional weight of full chassis might not be a big cost difference.

Just got an '06 Trademark 60.  At power-on, there are continuous popping and whooshing noises.  Consistently, it goes away after about six minutes.
Power cycle and the noise returns but then lasts less than a minute; unless the amp's been powered for an hour or more-then it's fine after restart.
All other functions work and amp sound normal except for addition of noise.
If I plug guitar into the effects return, the noise stops and guitar sound is fine.
Cleaned all the jacks, visually inspected PC board, jumpered the FX loop jacks (no effect on noise).
Channels settings, boost level and reverb level don't affect the noise level, but master EQ does. The character of the noise doesn't change-just how loud it is proportionate to the EQ cut or boost.
Tech 21 was responsive to my inquiry and said they haven't seen this before. Suggested I send it in. Being in California, the round trip shipping even for chassis only will be almost as much as the bench charge. Reminder: other than switches and some caps/IC's, most of the components are SMT. Comments welcome.

I know this is an old thread, but just got a Tramp that has the exact same issues as the OP.  Wondering if there was ever a solution to the channel switching problem.  I have tried all the various one and two button foot switches I own-none make a difference. I've touched up the main PC board with solder and it generally works well except for low frequency oscillation on the gain channel if reverb is turned up (new tank installed).
Thanks.