rectifier tube recommendation for champ clone

I'm adding a choke to my STF champ clone (has a way oversized output transformer and a bit extra filter capcitance) and later may add a second 6V6.

It's got a 5Y3 right now. I might even put a solid state bridge on a tube base... But what I'd really like is a better rectifier tube with a bit more voltage (less voltage drop) and more current capability, assuming such a thing exists.
I'm not exactly after less sag (or I would beef up the power transformer and go to solid-state rectifiers), just less loss and a bit more current at the rectifier, so that I can add better filtering and a bit more current storage.

STI makes a "super-duper" (my words...they call it Deluxe or a SuperCharged but that has other fender connotations of push/pull, which it's not) kit similar to what my entry-level kit is evolving into (two parallel 6V6 single-ended), except mine will have an even bigger output transformer and theirs has two rectifier tubes. I'm trying to get away with the same power transformer initially, so it will have a LOT of "sag" when I push it hard. But I'm adding chokes and caps, so it might be pleasantly clean and even 'chimey' at lower volumes.