Why can't we join two A2 units together, the same way we join an A2 and a B2 to get a D4.8.4? The edges of the A2 unit that connect with the other unit (the edges on the skew-polyhedron boundary) all have dihedrals of less than 180°, so I think if another A2 was added, those edges would all exhibit positive angle defects (sum of the dihedral angles would be less than 360°).

Also, I think I found a new CRF, but given my track record, it'll turn out to have a flaw.

It has some vague similarities to a D4.8.x, but with a different skew-polyhedron boundary... (Important note - I was only able to find one unit that could fit into this boundary, so I joined two of them together. If the reasons that prevent us from joining two like units of D4.8.x apply here, I guess we can stop this expedition early.) The boundary is best described as a "square rotunda," which I think can be represented by, among others, the lace notations xoM4ofx (M ≈ 0.6702), Nox4ofx (N ≈ 0.7962), or xox4oPx (P ≈ 2.0838). The 4D "top" of the unit is a square, and with two units extending out in 4D from the boundary, the entire polychoron resembles a "dipseudopyramid."

In total, it has 28 cells: 2 cubes and 2 squacus, 16 squippys, and 8 peppys. Of its 24 vertices, 16 are part of the square rotunda, and the other 8 are part of the terminal squares.

Hopefully I learn an important lesson when it turns out not to work, although I wouldn't mind if it actually did work...