> can run 6V6, 6F6, etc, so it needs to be fixed bias.
Doesn't "need" to be fixed (actually user-adjusted) bias.
Stay with the classic tubes. Don't go too close to the voltage and current ratings of the smallest ones. That means using transformer impedance suited for the smallest of the set. Check pinouts, there are some small differences.
If you use 250V on the plate, a bit less on the screen, 8K-10K load, and a 470Ω cathode resistor, and check pinouts, you can swap-in any of 6F6, 6K6, 6V6/6AQ5, 6EY6, 6EZ6, 6L6, 7027 and even 7591 and 6550 without re-biasing. All of these will wind up at about the maximum power point for 250V B+ and 8K-10K load.
Of course it is a little silly to take 3 Watts from a mighty 6L6GC or 7027. But to get more power you not only have to change the cathode resistor, you have to change the load impedance and often the B+ as well. 6L6 will make a lot more power than 6F6 IF you drop the load impedance to 2K-3K (and re-bias for more current), and you can also (for 6L6GC) raise the plate voltage a lot.
What you will really find is that all tubes are nearly the same when worked at the same B+ and load, and an appropriate current. There are three main classes: US pentode like 6F6, the 6L6, and the euro KT pentodes. A 6V6 is very much like half a 6L6, and if you run a 6L6 at 6V6 currents and loads you may not be able to tell them apart. A 6550 is not so different from two 6L6. In single-ended, the 6F6 will make less even-order distortion than the 6L6/6V6 family. Most of the KT series will have less abrupt clipping than the 6L6 family. But if you design an amp to take "any tube", you have to design for the smallest of the set, in which case the bigger members of each family sound and bias almost exactly like their smaller kin, just eating more heater power to support the current you are not asking them to give.