When whipping cream, does its state continually cycle through various states? Is there a dead end at whipped butter? Or does something else happen?

From the article you linked to, on making butter:

... what you're ultimately doing is smashing those little globules of fat into each other, damaging their walls and causing the hydrophobic (water-fearing) regions to clump together. The cream will become thicker and thicker as more and more fatty triglycerides gather into one mass. Eventually, enough fat is exposed and there's room for everyone to get together, eliminating the need for triglycerides to partner up with air.

This is not a reversible process. The fat globules are broken and the fat's released. You can whip the fat up to make whipped butter, you can make emulsified sauces out of it like you can out of butter, but you can't turn it back into cream, just as you can't make cream out of butter and milk.

In order to actually produce butter, you have to drain away the liquid, and possibly knead it to bring together fat crystals from the free fat and firm it up. (For more detail on the structure of butter, see this answer about melting and resolidifying butter.) You haven't done this in your process, so you have very soft butter (no large fat crystals) and buttermilk.

If you whip it with the liquid still in it, you may be able to produce very soft whipped butter, and you may be able to get a decent amount of liquid whipped into it, but they won't be bound together and they'll be very prone to separation. Normal whipped butter is just whipped butter, not whipped butter and buttermilk; whipping doesn't really make butter able to mix well with liquid.

The only other thing increased whipping is going to accomplish is breaking down the cream even further, releasing fat from the fat globules that escaped the initial whipping. That'll mean your buttermilk gets even more watery (less fat globules left in it). And your butter will be more free fat and less fat globules. Both of those are soft, so the butter will still be very soft. I suppose if you then drained it and kneaded it, you might be able produce an even harder butter than normal, since there's more fat available to form larger crystals from, and less globules to soften it. But that won't happen from the whipping you're asking about.