Try looking up fellow Pinsider 'Too-many-pins'. He has a pin business with a lot old stock. He posted about selling it recently, but he might still be taking orders. I just PM'd yesterday about some old Williams plastic rollovers and he did reply.
OK, now if you REALLY want to wind one, I can chime in (some). I use inductors in my designs, but not so much transformers - so clearly not a magnetic expert. But I've wound many an inductor over the years on cores that are used at high power, so I have some of the 'oh crap' trophies when I screw up. And they are at RF, not lower freqs.
Here's what you need to do:
1) Remove the transformer.
2) The schematic shows a single winding on one side, tapped windings on the other side. Measure the inductance of each winding. Leave the other leads unconnected as you measure. I just got a cheapie analyzer on eBay for $20 that measures inductance (and other things). No clue about accuracy of the inductor measurements. (But wow, it correctly identified 3 transistors and determined they were OK and even indicated beta). I plan on taking it into work and comparing.
3) Now here's the problem area: You would need to determine the permeability of the core. One way to do that is to count the windings and work it backwards. Pretty much defeats the purpose since now you would be tearing apart your only transformer. You could maybe 'wing it' and guess, but another issue is the core could saturate if not selected correctly. Might be ferrite tho since the transformer is at low freq. And you'd have to find a core too, might not be easy unless you don't mind changing the footprint..
So, option 1 (contact Too-many-pins) is a better choice, at least initially. Only pointed out the steps that if you absolutely had to wind one, it can be done.
BTW, KB9TAF here (if the FCC renewed my license!).