They used transformer coupling in these sets as it gives more gain. R/C coupling will generally give better fidelity but less gain; however, you may be satisfied with the volume you get, and on a typical twenties speaker, the better quality may not be noticed anyway!

The volume is really good, in my opinion. I was surprised how loud it goes.

Are you listening through headphones or a speaker? I've found headphones (especially Baldwin type Cs) much better for critical listening on these 3 dialers.

Thru a speaker, with a good range of volume.

transformer teardown
 

Heres some pics of the transformer, the first is the temp circut I hooked up to test the radio, next is the coil of the tansformer. One winding is broken internally. The last pic is all the pieces of the transformer.
What I'm doing now is cutting the center tab out of each plate, so when it's assembled, it will be hollow to mount the resistors and capacitor inside.

The replacement core should fit on your transformer, as yours looks pretty standard for that era. I've seen little bits of wood used to snug up the fitting between the windings and the laminations. Don't expect a huge difference in performance. I replaced the transformers in a Neutrodyne set, after bypassing the originals with an RC circuit, and didn't notice much of a difference either way.

I'm not replacing the core, I'm putting the RC circut inside the transformer case.

here's he gutted out transormer with the 2 resistors and capacitor mounted inside. I think it turned out real nice.