Can I wire the secondaries of 2 high-voltage transformers in series safely?
No. You cannot safely series the outputs if they are standard Neon Sign Transformers (NSTs).

The standard transformer is built with a centre tap on the secondary, which is designed to be grounded, and may even be permanently grounded in the case.

This is so the two ends of the secondaries only need to be insulated to take +/- 3kV from ground, x2 for a factor of safety. The turns around the centre tap are only insulated to cope with the safety factor of mains connection, typically 1.5kV.

If you are able to disconnect the centre taps from ground and put the NSTs in series, even the lowest tension way of doing it which is to ground the new mid point, then the insulation at the old centre taps and at the far ends will be stressed beyond its design value.