That's correct. I don't know if that's the same for both the single-ended and balanced outputs, but I'd imagine it would be.
You've got a really good puzzle here
I'm going to assume your hearing is equally good in both ears (that's probably not true for any of us, but let's roll with it for now). The fact that the issue seems to follow the right earbud suggests it's not the cable alone (though it might still be good to clean all connectors and measure boths sets of L and R wires separately with a multimeter). It seems to me most likely an issue with the MMCX socket on your right earbud not properly seating the balanced cable plugs, or, just maybe, some mismatch between your L and R buds that you're only noticing with a higher-impedance cable. I'd go with the Deoxit first, because it's cheap (at least in the US!) and will always come in handy another day. If you notice any hint of crackling or drop-outs with that balanced cable, I'd definitely also take that fine-grit sandpaper to your balanced-cable plugs (as in my previous post).
If that doesn't fix it, I'd look at getting yourself a better balanced cable (if you really believe in balanced outputs that is - but that's a question for another day). IMHO, 0.8 Ohm is a bit high for a piece of wire. My Ag litz cables are all about 0.2 Ohm, even with a 2.5->3.5 mm adapter connected. 0.8 Ohm (and 0.94 Ohm) might not sound like a lot, but this can be a bit too high for the SE846 (or Andromeda), given that they're only nominally rated at 8 Ohm based on their response at 1 kHz. Their actual impedances vary with frequency and both drop below 4 Ohm in certain locations:
I left the L and R SE846 measurements separate to show that these things do come with some small unit variance. A higher cable impedance from your WM1Z could create a shift which shows up more strongly on one channel. Something also to note... you said you'd not heard any effect with other earbuds. Andromeda should also show a shift with higher impedance source/cable, but its response, and what you'd need to be listening for, will be very different. You can (roughly) consider the impedance curves to be the shape of the EQ you'd apply when increasing z-out. SE846 tends to get darker, whereas Andromeda tends to get brighter. Both are arguably aberrations, but if you provide a boost at 8 kHz (Andromeda), and can overlook the fatigue and changes in timbre this causes, you typically
will hear more detail, so it can lead people to either not worry, not notice, or to think their cable is actually doing something magical. BTW, the effects of cable impedance on the SE846 can easily be measured, even with the cheapest of couplers:
https://www.head-fi.org/threads/shure-se846-impressions-thread.675219/page-1207#post-13644650
My best guess is that you need some Deoxit on your right earbud mmcx connector and/or sandpaper on your balanced cable plugs. Plan B - I'd try a better (lower-impedance) balanced cable. And, Plan C - in an ideal world, a DAP with lower z-out and no silly proprietary balanced connections
I'm curious to know which of these (if any?) fixes the problem. Please don't keep us in suspense for too long... Good luck!