Thanks. That was actually just a mistake. The full schematic LinkedIn the original post had it connected to the correct side of the shunt. Also the full schematic has op amp compensation. The schematic this post has been working off of is Justin trimmed-down version for the purpose of my original question. Which unfortunately still has yet to be answered
Okay, the link... would've been helpful to include a snippet of that rather than the other thing.
So, let's see here... yes, they do indeed have compensation, very nice! But...
what the fuck? They literally have the opamps upside down! Minus to plus! Positive feedback! The pin numbers aren't wrong, either! It's really wired that way! Who drew this!
It doesn't have a layout either, just a bunch of stuff scattered around... what is this!
Incomplete, I guess, but how many times do you really have to cook and re-cook a stupid
LOAD circuit? I know some companies are very "not invented here"-averse, but the kind of people that keep doing these (and homemade bench supplies, and..), man...
In short: answering the original question is much lower value to you than addressing the mess, that is whichever of these schematics -- the thing has to
work before you even need to think about trimming out millivolts and microamperes. And tempcos and drift and precision. And anyway, it's a LOAD, what does precision matter? An SMU sure, but that has inputs and outputs, and wide dynamic range, and programmable control so it can do quite a lot of things, automated. That's a lot more work than rubbing two opamps together.
So that's fundamentally why you hadn't gotten an answer yet.
But anyway, to answer your question properly: no, you don't need negative supplies to deal with Vos, because Vos is an input-referred spec, not an output spec. You have to look at V_OL and V_OH for output voltage range. Typically a RRO amp can swing within 10s of mV of the rail, which is good enough for most purposes. If you need a very accurate zero, you can just as well bias up the shunt feedback signal instead (which has to be done per transistor-amp, because the master amp can't force them to zero).
Remember that an opamp senses an input voltage
difference. Adding an offset to one input is the same as subtracting it from the other. This can save you a lot of tiddling with -1.5V supplies!
On that note, I'd be happy enough with TL2372s instead of NE5532s, and eliminate the -15V rail altogether. No need to burn so much supply current, on an ancient and mediocre audio opamp, and certainly no need of a +/-13V swing at the gates. A +9/0V swing is more than enough, and helps limit transient short-circuit current draw.
HTH,
Tim