I'd definitely try running 4 new EL34's first and foremost, making sure they're biased nice and hot (not too hot though!). If that doesn't pickle yer sonic fancy, you can then try swapping out one of them mid-bite, borderline harsh V30's from the open back cab to something creamier... One of the original Ipswich made Celestions that can handle the power, or even a Jensen Blackbird or as mentioned, a Celestion Gold Alnico...the latter two are the epitome of old school smoooooooth. I'm in LOVE with Gold Alnico's.
After that, yes, there are some ways of smoothing out the gain - all in the preamp section. But we can discuss this well after the above two mods have been looked into. I think you'll find the EL34's are really the bomb. I'm a huge fan of them, and was hesitant about going the 6550 route, but the 6550's surprised in the their "new" approach to sound - loud, crisp, surgically tight, and excellent bottom to top spectrum - but ya, they can sound a bit clinical - so be it, for my purpose now, that's fine. SED Winged C EL34's are rich and not too expensive. Give 'em a try.
Peace,
V.