So it's not possible to wire these backwards for negative voltage as they would end up as high-side instead of low-side as they are supposed to be? Or is this only a problem because the supplies share a GND rail?
It should be possible, but not in a nice way. Take your previous picture:
+ / "red line thick" connected to the common ground between your two regulators
- / "black line thick" connected to the LM337 negative output rail
"yellow line thick" gets connected to the negative output terminal
"black line thin" also connected to the LM337 negative output rail. This is actually annoying, using the LM337 input would be nicer, but I don't see a way around it,
under the assumption that the thick and thin black "lines" are internally connected in the meter.Then
Variant A): "red line thin" to the common ground between your two regulators. This effectively means you can't go below -4V output on the negative supply. Otherwise the meter is no longer properly powered.
Variant B): An additional (positive) 3-teminal regulator, probably even with a pre-regulator, because of the large voltage difference. Regulator's input coming from the positive input rail (i.e. the one going into the positive LM317 on the other part of the supply). Regulator ground connected to the LM337 negative output rail. "red line thin" connected to that new regulator's output.
Variant C) Same as B), but just a beefy resistor and a suitable zener, to build a simple regulator from the positive input rail.
In general, it would be easier if the input -17V/+17V voltages would be completely isolated.Then you could just build two identical LM317 regulated supplies, and just join the negative output terminal of on of them with the positive output terminal of the other.
You will also have the problem that the shunts will introduce a current-dependent voltage drop that can't be compensated by the LM317/LM337. This is a problem because of the way the LM317/LM337 work.