Wow, thanks for the input everyone!
Just as I suspected, each of the different ways I've thought of to get the job done was presented back by those of you taking the time to reply.
For example...
John talking about coming at it from a fabrication perspective. Yeah, I work in a weld shop, and have considered just forging a "bottom cup" without the hardy shank, and welding it a top tool blank.
Pnut saying to use a ball hitch. In fact, when I forge a cupping tool, I use a large ball hitch that I cut the top 1/3 off before grinding the radii, so that the thickest part of the ball determines the width of my cupping tool, without making the depth 1" (since a 2" round billet is usually the largest hammers I make")
JHCC and his agreement with Lisa about not storing thread in his shop. This is also high on my list, seeing as I don't particularly like it when Lisas yarn gets near my forge.
Anvil: you are my hero, and not just because your user name is Anvil, but because you did the bullets list. Also I think you're onto something about taking a hammer blank and upsetting it into my bottom cup to make the die (for lack of a better term) to use to create the top cup.
Littleblacksmith made a lot of good points that I might have assumed was common knowledge, and not worth bringing up. I've spent a lot of time with Brian Brazeal, and even though learning from him is like drinking from a fire hose, one thing he drove home about the face of a rounding hammer a lot with his quote "It's not a sphere! It's more of a... squished ball shape". And even though I suggested he call it a "lens or lentil shape", I'm sure he's out there right now still saying "squished ball".
And before even reading Littleblacksmiths post, I've already welded up a new swage block with a hardy shank. The swage is about 3" deep, and 1.25" square, so that I can upset stock, almost identically to what Torbjörn Åhman does in this video.
From there, my plan is to use the hammer blank upset into the bottom cup like Anvil suggested and drive it down into the upset face of the billet in my fab'd swage block hardy tool to create the impression. Once it's going in the right direction, I'll take it out and tap on the sides of the cup to intentionally fish mouth it, just as Littleblacksmith pointed out. If the fish mouthing goes too far, dropping the billet back into the swage and knocking the edges back out with the rounded hammer blank should dress the tool out.
Done!
...well, except for letting the face of the tool hang over the edge of the anvil while punching and drifting the eye for the top tool. But that steps never been a problem on any other tools of that general shape