So it looks like the best spots to farm for relics are:
Lith - Taranis [Super low level defense, hoping it's a trivial 10-wave solo for my Equinox build I normally farm Meso relics on Io/Jupiter with]
Meso - Belenus [Another defense, more like Hydron level though so you'll want a group and it's probably even half decent for formaing shit if you're boosted. Only stay 10 waves though, B-rotation is all Neo. A-rotation is annoying too since it is Meso/Neo split.]
Neo - Mithra [If you're lucky you'll have all the Neos you need from doing Belenus and whatever you choose for Axi, but if not the fastest way is Mithra. This is a high level interception though, so YMMV in pugs. Not sure if Limbo can cover multiple nodes with a max range bubble here... maybe two but I'm not even confident about that. If you don't want to deal with pug interceptions and can't get a premade going, just stick with Belenus. Mot is an option too, if you're confident in your ability to do a 40-45 Void survival.]
Axi - Aten or Marduk [I hate Orokin Sabotage much more than Mobile Defense, so I'll choose Aten. You're going to get a bunch of Neo relics from either of these missions so do this before Mithra or whatever. That said, if you have a super efficient Mithra premade, it's probably worth going on to C-rotation there for your Axi too.]
Still torn on whether or not to just buy the rhino pack. If they weren't so stingy with the 400 plat I'd go that route for sure, but since I only need 5 common, 4 uncommon, and 2 rare parts to make Rhino/Boltor/Ankyros I guess I'll slog through Void missions for a while before giving up.
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Unrelated, Saryn is apparently getting another stupid and unnecessary Miasma nerf because she can 4-spam low level missions no one cares about. If Pablo fixes the bug where Miasma doesn't actually do extra damage to infected mobs it might not hurt too much in ESO though.