How to split pre out to connect power amp and sub

The thing you CAN do to hurt a tube output transformer is to put too high an ohmage load on it. If you open the outputs, the energy that gets stored in the magnetic core has nowhere to go if there is a sudden discontinuity in the drive, & acts like a discharging inductor. This can generate voltage spikes that can punch through the insulation inside the transformer & short the windings. I would not go above double the rated load on any tap. & NEVER open circuit the output of a tube amp - it can fry the transformer in a couple of ways.

It's almost never low impedance that kills an OT, it's too high an impedance. The power tubes simply refuse to put out all that much more current with a lower-impedance load, so death by overheating with a too-low load is all but impossible - not totally out of the question but extremely unlikely. The power tubes simply get into a loading range where their output power goes down from the mismatched load. At 2:1 lower-than-matched load is not unreasonable at all. If you do too high a load, the power tubes still limit what they put out, but a second order effect becomes important.

There is magnetic leakage from primary to secondary & between both half- primaries to each other. When the current in the primary is driven to be discontinuous, you get inductive kickback from the leakage inductances in the form of a voltage spike. This voltage spike can punch through insulation or flash over sockets, & the spike is sitting on top of B+, so it's got a head start for a flashover to ground. If the punchthrough was one time, it wouldn't be a problem, but the burning residues inside the transformer make punchthrough easier at the same point on the next cycle, & eventually erode the insulation to make a conductive path between layers. The sound goes south, & with an intermittent short you can get a permanent short, or the wire can burn though to give you an open there, & now you have a dead transformer.

So how much loading is too high? For a well designed (equals interleaved, tightly coupled, low leakage inductances, like a fine, high quality hifi) OT, you can easily withstand a 2:1 mismatch high. For a poorly designed (high leakage, poor coupling, not well insulated or potted) transformer, 2:1 may well be marginal.