I got busy and haven’t updated the thread so I’m just now responding
I found Waldo.
Forza 1700-1
I ended up ordering this set. It’s ridiculous expensive and is on the slow boat from what I’m hoping is Europe and not China for the price. I’ll update once I actually have it in my hands.
This is an OTC 949-1/2; the edges taper out to very thin and the back is flat, I would be surprised if it didn't work. As far as the bearing that's recessed, maybe dry ice on the other end of the shaft and a miracle?

My el cheapo splitter was far from flat on the back side. So tossed it in the mill.

Ended up taking .1120 off of it. It’s flat now and works much better. Guess the cheap tool is now the quality of expensive one and actually works like it should now.

At some point I’d like to pick one of these up if I can ever find a reasonable price on one. Way better design.
I think the problem with modifying the pullers you bought is that once the arms can get under the bearing, that part is now too small to grab the bearing. Maybe you could add a hose clamp or some other clamp around the arms to get them to grip? Maybe good enough to do a few anyhow.
It seems like the real solution is going to be a collet of some sort.
I like the hose clamp idea. Will try that on the next batch. Hopefully the puller above arrives soon.
I machined a jaw puller down to work.

The pot metal that puller was evidently made of was soft as butter to machine. We will see how many uses I get out of it.

But it’s working. Just down have high confidence in it lasting. Bunch of crud under that bearing too.
What manual / catalog are those tools out of? If my lathe was powered up I’d make one and add two bolts to pill it together however it’s not getting wired up till I get into my new shop with 3PH and that buildings not going to ready till January at least.
Parts are available individual to make up a small puller if need be instead of buying a whole set. Perhaps the small ones would work?
That set you posted looks like all of the parts are way too big.
So the search continues. Hopefully the puller I ordered works. But given the volume I have to do, it would be a good idea to have multiple options.