Have you considered having that transformer rewound? The construction lends it's self to that being doable for a profesional, and that may be the only good option for a rare part like that.

A transformer isn't rocket science. I have fixed many transformers. All it takes is a bit of patience.

I suspect all that is wrong is the lead has broken from the terminal board and simply needs resoldering. Otherwise the winding may be repaired, especially if it is the outermost winding. I generally find the lead broken under the uppermost paper wrapping.

Finding a replacement for a TK31 is going to be near impossible. Rewinding will be the only solution if the problem is not obvious.