[Ron Ramirez]

...Oddly, the primaries on both interstage transformers were bad, ...

Not so odd. Actually, bad interstage transformers in 1920s battery radios are the rule rather than the exception, and it has been this way for decades. That is great that you were able to "freeze" out the insides of the originals!

There is a simple solution to your dilemma. If your transformer wires have the same color coding as the Hammond 124A, then simply measure with your multimeter set to ohms, across the red and blue leads. If you get around 400 ohms, that is your primary. Measure across the two green wires and see if you get around 1500 ohms, and measure from the black lead to each green lead (in turn) and see if you have continuity. If so, you've found the secondary. Then, take notes so you won't forget which wires are for the primary and which are secondary...and proceed with the installation.

Good luck! It should be a really nice radio once you are finished.