... Switch pops like a banshee of course too! ...
Sure it does, because you're switching the coupling caps from one d.c. voltage to another (and a fairly big voltage jump at that). There's no easy way to stop that popping.
There is a "hard way" in which the switching is done by JFETs (or perhaps optoisolators) instead of a mechanical switch, but then you need solid-state switching circuitry to control those. And ideally the control circuit would fade from one output to the other instead of instant-switch. So it can be done, but unless you're adept at building such circuits (or find just the right kit, which will be challenging), this will seem hard.
... Does not loading one of the taps (i.e.- when the switch is thrown and one set of caps is just floating) cause any ill states? ...
Nope. If you connect nothing to the cap, the tube feels as though the cap is not even there.
I suppose it's possible if you have very long wiring from one of those outputs looping around the chassis and near a high-imedance, low-level stage earlier in the circuit that you could get the unused wire to create oscillation. But I think the chances of that are fairly remote.
... I think that the output impedance of a triode stage is calculated with Ra and ra in parallel from the formula:
Ra X ra/Ra + ra
The output impedance will only be relevant for the triode connected to your preamp's output. Then it matters because you'd like to have an idea of the cable capacitance being driven (so you know how much treble will be knocked off your signal), and also because the transformer primary may look like a heavy load to a typical plate output which then knocks down the gain of that triode.
Are you using the transformer you have as a plate load (i.e., transformer primary instead of a plate load resistor)? Or are you trying to use it as a matching transformer (triode has a normal plate load & coupling cap, and the transformer primary is after the coupling cap)?
I suspect a 6SL7 won't manage to drive low impedances well, and possibly not long cable runs without treble loss. What are you hearing when you try the preamp/DI with a long cable on the output?