Should separate the shared bias resistor and double the voltage for both? ...
If you do it my way (switch to open the connection from the 0.1uF to the 470kΩ/6V6 gid), then you don't do anything to the existing cathode resistor.
If you do it the way you were originally thinking, you need to give each tube its own cathode resistor, and that resistor should be double the value which is in the amp now.
... Do most PP trannies have the air gap in SE mode ...
A transformer is either designed/built to be a single-ended transformer, or to be a push-pull transformer. Only SE transformers have air gaps.
Why?
A transformer passes power from primary to secondary by virtue of a magnetic field which is transmitted/sustained by its magnetic core. Current causes the magnetic field, so the idle current of a single-ended stage passing one-way through the transformer "eats up" some of the transformer's magnetic capacity.
To cope with this, a SE transformer has an air gap, and also uses a larger core for a given amount of power.
Said a different way, push-pull has the idle currents flowing from the mid-point of the primary out to either end, and so balances/cancels the magnetic flux of the idle current. As a result, it doesn't need an air gap. Further, because the core's magnetic capacity isn't being eaten up by idle current, the core can be smaller for the same power throughput and bass response. Said yet another way, this makes P-P transformer smaller and cheaper for a given power.
You might find a "universal" transformer claiming to be able to be used both in SE and P-P mode; in reality, it is designed for SE operation and doesn't realize the economy or weight savings of P-P.
Which brings us back to my suggestion. It might look odd at first, but allows you to buy a lighter & cheaper push-pull output transformer intended for 6V6's. When you do not drive one side of the output stage, it still idles and reduces magnetic flux in the OT primary (and hum due to power supply ripple), yet you still have true SE operation.
Some may argue you won't realize the best loading of the remaining tube for maximum output power, but I offer that maximum output power isn't why you decide to run SE in the first place.
I'll also acknowledge now I shamelessly stole this idea from Kevin O'Connor.
