I guess this one has a EL-84 on the other side and a 6V6 on the other side of the push-pull OT?
This doesn't have to be the case, but the 6V6 and the EL84 generally find close to the same optimum load with a given plate voltage. So yeah, they are probably on opposite side of a push-pull OT, judging by the claimed 15w rating (if accurate) You'd get a bit less than that in parallel SE (although you could do it that way too).
Separate cathode resistors + caps for the tubes and I guess the input signal to the EL-84 should be cut down a bit to match the output of the tubes a bit closer?
I'd guess seperate resistors and bypass caps, because cathode bias is the eaisest way to get this done. And yeah, the EL84 will need less bias at the same operating point, so it can handle less input signal before distortion. But I'd imagine having one side distort before the other would be part of the magic recipe for this arrangement.
If I were building it, I'd probably try a master before the phase inverter or a volume put between the phase inverter and 1 output tube only, and see which I liked best. Good balance and identical operation is easily achived and heard in amps using the same tube on each side.
Besides, the Gm of the tubes are different, so they shouldn't respond to input signals the same way, even if you "level-matched" them with the differeing bias in mind. Something that occurs to me is the current contributed by each side is likely to be different, giving the net result of a standing current flowing through one side of the OT or the other. This isn't a problem, but you might want to plan on a larger core than normal or an air gap to help handle this. If you're thinking about a build, you may want to contact a transformer manufacturer and ask aboput a product that can handle the resulting d.c. Exactly how much it will be (which is what they'll need to know) would require at least a basic design and an examination of how the tubes work together.
Or maybe I'm being over-cautious. They might track somewhat well; but a Gm of 5000Umhos in one tube and 8000 in the other makes me wonder.