Majors can be a major pain. I would start by increasing the screen
resistors. The stock ones are 250 ohms 25W. I added 1K 25W
resistors in series with the stock resistors for a total screen
resistance of 1250 ohms in the last Major I reworked. If you have
an o-scope & sine wave gen. look closely at the output. Majors
are also famous for frying their o/t's. The one I repaired had an
oscilation on one side of the wave. I sent the o/t to Bennett
Transformers in NY and had them rewind it. I put a set of KT-90
tubes in it and it rocked. Output was around 180W even with the
increased screen resistance. With the increased screen r's it should
be stable with modern KT88's. I would avoid Chinese ones
though. Make sure your filter caps and bias supply are in good
condition also. They can be death to tubes when they fail. 
 
RE

Make sure your tube sockets are 'clean' after the light show. You
may also consider the Hiwatt/Traynor idea and after the choke
have a 500-ohm/10-watt resistor feeding the screen grid resistors.
Should your screens try to draw excessive current when 'driven
hard' and attempt to arc, the 'sag' will end that arguement right then
and there. Works for me. My last tip is watch your VOM. I've
fried more than one VOM on Majors because of parasitics. The
lead dress isn't the best.