[Chas]

Swap the coils and the tuning condensers. No worries. IMHO the range of tuning may be greater in the AC model as opposed to the early DC model. Besides corrosion can be going on in the 35 coils that could manifest itself later.

How are the 35 audio transformers? If replacement is needed try to get OEM or at least try the ones from the 37. Often the first audio is 5:1 but not always.
Do not judge ratio by the DC resistances. Use an audio oscillator at either 400 or 1k with 10k isolation and measure voltage gain on secondary with VTVM or 'scope. Primary DC resistances are important for proper function of driving tube as well as detector, insufficient load = distortion.

I also suggest chasing the threads in the case for the bottom plate. These often freeze the screws resulting in the threaded insert turning in the case. Hold the threaded insert from inside the case when running a tap through.

Note: Setting up tuning bands, a small amount is "slop" in turning the master to each of the outer tuning condensers is by design. Since there is no tracking adjustment, "bumping" the tuning knob pushes the outer tuning condensers back and forth, user listens for best peak. Further: The single bearing in the tuning condensers is a cone, held in place (seated) by a phosphor bronze leaf spring, too tight of bands will force the cone out of place by overpowering the leaf spring shifting the tuning condensers value disproportionately. Some tuning condensers may not have the leaf spring but the "slop" must still be present. The mounts for the tuning condensers should be slotted with a lower slot on the main bracket to insert the blade of a screwdriver to correct the adjustment. The optimal alignment frequency is usually 1mhz, but if better reception on shorter wavelengths then lower, set shaft alignment frequency to 950 to equalize response across the entire BC band. A-K recommended lubricant is Nujol a mineral oil and petroleum jelly for the rheostats...

Another bit, use 6 volts for the "A" that establishes a consistent cycling of thorium in the tubes, then, if overall gain is low with all other bits of the circuits correct, and good tubes try reducing the values of the grid resistors in 100 ohm steps, when the RF stages become unstable, go back to the last resistance value used. DO use a short direct ground to EARTH not the AC line or the bed-springs, 50 to 75 feet of antenna up at least 10' to 35 feet should be fine, there is voltage gain in the tubes and each RF coil so there is ample sensitivity in most suburban locations...

YMMV

Chas