Yep, chalk that one up to poor design...The amplifiers are going out of balance during power up and down. Two seconds is pretty long... Try turning down the gain during power on and see if that affects it.

The pop on turning off is normal... None of these have speaker disconnecting hardware that is necessary for very high power amps. The biggies have hardware that checks amplifier is balanced before connecting the speakers and a relay also cuts the speakers immediatley on power down. As power goes up and down the circuitry comes to equilibrium and until it does, strange things happen.

I would investigate the CONDITION of the filter caps for the main power because if they age to a higher internal resistance that COULD cause the high freq oscillation on power up... Two seconds is MUCH too long.

There should also be some non-electrolytic caps NEAR the power output transistors to handle high frequency supply power bypassing.

Check the power bypasses that service the preamp stages. Look for pregnant electrolytic caps that have failed.

Ultimately, you MAY need an oscilloscope to isolate the high freq problem.