Baking might improve the megger reading, but won't fix the problem of 1/2 output voltage. Nor will remagnetising. If you're getting to 1/2 voltage, there's plenty of residual magnetism.
Here's what I'd do: First, I'd set out to prove that the stator main output windings and the field coils are OK. To do this, excite the field with a DC supply, of whatever the rated field voltage is (about 48V DC on some that I've seen, but yours may differ - hopefully the field rating is on the nameplate.).
If this tests out OK, meaning you can get rated AC output with nominal field excitation, I'd proceed to buy or build a solid-state voltage regulator and simply not use the "harmonic winding'. If you can't get the rated AC output with nominal field excitation, it's probably scrap. Has anybody here ever rewound an ST head? I have my doubts, but jump in if so. Having a motor shop do it would be prohibitively expensive on a 3 kW ST.