No problem - this is very important to me, but it is not very urgent at all. I definitely think it should be fixed, but as far as I'm concerned, there's no big hurry - so by all means, please take all the time you need. I hope your health improves soon.
I've tried the "use full precision UVs" option and yep, it fixes ALL the alignment issues I've described - including the warping, so now you can have faces of just about any shape (I haven't tested n-gons much, but all quads and tris are fine now) and everything aligns nicely between different faces and across separate meshes. As far as I can see, as long as this option is selected, the textures in UE match what you see in Hammer with absolute perfection.
Like you said, it's quite a nuisance to apply this to each mesh separately; in my case, it would be feasible, but I'd just... really rather not do it. I understand that applying this option to every single mesh would presumably have some impact on performance/memory, but I think it's absolutely worth it for me. So if you could indeed make HammUEr do this automatically during import, I'd be immensely thankful for it. Maybe it should be optional, but I'd always leave it on anyway.