• WARNING: Tube/Valve amplifiers use potentially LETHAL HIGH VOLTAGES.
    Building, troubleshooting and testing of these amplifiers should only be
    performed by someone who is thoroughly familiar with
    the safety precautions around high voltages.

microwave MOT as SE output transformer

Since the devices are from consumer electronics (kitchen appliances) I'd expect that their laminations are selected for cost (M22 or worse) as opposed to M6/M4 steel. The core losses and distortion at >1kHz are probably not great.
 
MOT cores are slow. They start to distort sine waves from about 1kHz and upwards.

Below are traces from an Arch Nemesis, a MOSFET driving an 8:1 OPT made from MOT cores. Top trace input, bottom trace is output across the secondary, feeding an 8R load.
 

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I can't see a concern with using them for SE. Afaik, the secondary would be your SE primary, so perhaps do a turns ratio test to see if they are close to 10:1, which may then allow a 1k6 ohm primary impedance for 16 ohm speaker. That will then give you some idea of what output stage valves may be appropriate.

Afaik, a microwave oven uses a doubler rectifier, so the core isn't designed for DC operation per se, but likely has an incremental inductance that doesn't change much up until a certain application level of dc and ac. You could measure that using a relatively simple test jig such as in https://dalmura.com.au/static/Choke measurement.pdf. Measuring the primary winding inductance (ie. the HV winding) is important as it will then give you some idea of what your low frequency response could be. An even simpler measurement is just to use say a 12Vac supply and an AC current meter (or resistor for current sense), and doing the calculation.

The core construction is for cheapness, with a weld along the butted laminations. That does provide a form of gap, somewhat similar to what many PP cores use (eg. alternating groups of lamination directions) as a way to allow dc unbalance in a PP output stage, but not a significant gap aiming for a certain inductance as used by chokes.

Does your core construction include visible shunt lamination sections (eg. see https://www.qsl.net/kh6grt/page4/xfmr/pictures/transorig.jpg )? It may be practical to knock them out, as a way of reducing leakage inductance.

I wouldn't take post #5's results as generic until some better measurement data is presented.