Mullard EL34 that sounds best

I would recommend JJ power tubes https://www.jj-electronic.com/en/power-tubes

pro: very stable over long run time

Luxman Japan uses those for all noble tube amp designs 

The Avatar is a great amp. The new stock Mullards are very nice sounding tubes IMO compared to most. Do a google search and try to place the reviews of different tubes to your preferences. 
 

It appears that the older Mullards you go with the better, generally speaking.

The price from reliable sources, if they have them, and even from unreliable ones, is very close to prohibitive. $450 for XF1 each new or $300 for used, that's what I see. Some say, though, that NOS EL34 Mullards might last 5000 hours, which is great if true.

(any) tubes will last longer in gentle usage conditions, lower dissipation power / current / voltage increases ~ 20% spec degradation time point. to figure out how long tubes will last need to check amp design and tubes aging related spec.