Hey Dr. D, whats up. Well, I don't really think we're being nit-picky, we're just trying to make it work, though I guess it is delaying the Hex III from taking off. We've already done two Hex collabs, and they are essentially identical, in format. It's time to take this whole hex collab idea to the next level. It's worth the wait, and worth the effort.
This post doesn't cover how to make the end-result tile with itself for the infinitely tiling masterpiece that we all want to make work. That comes next, if these "hex blocks" are approved.
I'm still not satisfied with our research, at all. I just moved and have got my office back in decently working order, so I sat down to think about it a little. My contribution today isn't stellar, it just kinda states the obvious - using chunks of hex tiles to create, not an overall hexagonal shape, but rather more of a block that will very easily tile with itself. The overall hexagon shape of the Hex Collabs I & II don't play nice when you try to tile them, though it's still possible if you just do it manually.
The below image, using ptoing's miniaturized hex-grid posted above me, shows you the shape of each individual Hex Collab, then in color how they fit together, demonstrating easy tiling. Top right is just for reference - the real hex tile's size. At the very bottom are two more options for non-hexagonal tiling hex-tile comprised blocks.

Yes, with this idea, we sacrifice the wonderful design factor of the overall Hex Collabs all being hexagonal themselves -BUT- when they're put together into the final endlessly tiling image they're destined for, you can't see the shape of each Hex Collab anyway - the edges get lost, they're all put together, so it does not matter what shape they are unless you plan to break them all out and display them separately, which may be the case a few times, but the real priority is making them work with eachother; seamlessly tile.
Therefore this funky lookin' "hex blocks" idea isn't that bad, it's just not as cool as having each individual Hex Collab, used to create the seamlessly-tiling image, be a hexagon itself.
-Put your brain to work, post thoughts/ideas, we're approaching a solution-