I'm puzzled how you removed a 2-wire part and came up with three loose ends.
The schematic shows the thermal breaker between the black lead and the 120V winding.

I can't identify the black lead in your image; you can see it better.
A wild guess is that the black lead may come under the winding in the TB pocket; and the two thinner loose ends are a winding which broke in the tear-apart.
Inventory your leads. Check continuity against the schematic.
If indeed the 120V is broke and you can't figure how it was, you may have a hard time getting voltage numbers for MM.
Hmmmmm.... the 6.3V winding should be obvious because leads are green and winding is FAT, and the ohms should be much less than 1. Get another PT with a 6V winding, plus a 10 ohm 10 watt (Radio Shack) safety resistor. Try to drive the sick PT's 6V winding with 6VAC through the resistor. Check voltage on each winding. The source should of course be 6V-7V. The "sick PT" winding would ideally be the same, but really somewhat lower with the resistor. If it is a little low like 5V, take the resistor out and drive directly. If a lot lower, under 1V, the sick PT has an internal short (and the open 120 is a secondary problem).
Anyway: with something like 6V on the green leads, measure all the other windings. BEWARE!! The 120V and 400V will be lethal, use clips, don't trust fingers.
With power OFF, measure winding resistances (you can't measure the 6V heater winding any reasonable way).
Patrick will also need the 6VAC current demand to back-guess its resistance. Six 6550 is 9A-10, and two littles is another 0.6A.
And he needs the nominal wall voltage ("120", "230", etc).
Core dimensions (outside height width stack) are important. Also note which ones are mechanically critical (mounting holes, any limit on overall height) or if he can adapt to existing stampings and you'll find a way to mount it.
If you have micrometer, wire gauges would save Patrick a few moments.
Once Patrick picks a core stack, he can pencil the turns for 120V and a gauge that fills 40%-45% of the window. Then the 6.3V winding is nominally 1/19th of that turn-count, except there will be about 5% sag so it has to be like 1/18 or 6.6V unloaded to get 6.3V loaded. Similar calcs for the other windings. He'll want the schematic to estimate ~~66VA in the heater but ~~600VA in the plate winding, and allocate window-space in proportion to power. Back-calc gives the current. Turns and area and insulation gives wire gauge. There is a nominal current density. All these calcs will give answers which are never a whole gauge number or a convenient number of turns (you like full layers) so there is a lot of tedious round-up/down and re-calc to come to a producible design. And he might discover that his conservative factors won't fit Fender's core... that Fender designed it down to the razor's-edge of excess warranty costs, and it might be wise to go next-up on core-size for more decades of use.