Some extensive googling has shown me that both units identical looking unlabeled carts are in fact Astatic "Power Point" (hey microsoft someone was using that phrase) cartridges.
The Webcor 1054 apparently needs a 0.15V stereo cartridge (based on the .15VAC label on the internal schematic at the pickup input).
I'm not sure about the cart in the Warwick built Talking Book "reproducer" (giggidy) model AE 4, but it seems to need about the same input based on some comparisons.
I tried plugging an 80's component TT into the amps of both players...The Webcor barely had any output, and the TaklingBook was better but not nearly as loud as it should be.
What sucks is that I have an RCA 118 200-9 stereo cart (it looks like the one below) that has the output to drive both amps quite well, but the blasted thing is too wide to fit either tone arm...I was able to hook clip leads between it and the amps and set the bare cart on a record on either player to check output (which was LOUD and clear).
Most of the carts posted about so far are out of production and expensive. There is no way I'm spending even close to $60 a pop for cartridges for a couple of $10 phonos.
There ought to be some cheap current production cart that can tolerate tracking on the heavy side, put out ~150mV, and not cost more than twice what the phono it's going into did.