Thank you all for your input!
I took OP14 out of circuit and tested it in a unity gain setup, feeding a 10Hz, -5V to +5V square wave at the non-inverting input pins.
The power supplies where +15V and -15V.
And the results are interesting:
- Half of the IC (i.e. the one corresponding to IC8a in the schematics) is mostly working, although with quite a bit of noise introduced at the output.
- The other half (i.e. IC8b in the schematics, where we have been investigating our +15V source issue), it has an interesting behaviour - see attached picture (please ignore the slight offset for 0V for each trace; that's just my scope where I cannot run a full SPC).
That is an interesting failure: when the non-inverting input goes negative, the output & inverting input go positive, to almost +15V.
I've just realized something: could this be a short to the positive rail when the non-inverting input goes negative?
Anyway, this confirms OP14 is toast, so I went ahead and ordered a replacement OP200 (thanks,
ch_scr), as it was also more easily available to me and at a decent price.
I will keep LT1013, OPA2202 and ADA4077 in mind (thanks,
Alex Nikitin and
Kleinstein), in case OP200 turns out not to be a good replacement.
And since I was investigating that area of the circuit, I decided to remove and test IC2 - a DG211 quad analog switch IC.
The IC turned out to be ok for 3 out of the 4 switches - the 3rd switch was constantly off, though, no matter the input.
However, that would have had no bearing on our initial problem.
Still, I've ordered a replacement DG211.
shakalnokturnI considered the possibility of IC2 leaking via its inverting input pin, but it looks like OP14 was the main culprit, as per above.
Andy WatsonI suspected TR5 might be bad but, based on some initial tests, it seems to still be ok.
However, based on the experience with OP14, the reliability of my initial tests doesn't look too good at the moment.

I'll check it again, just to be sure.
If it is indeed dead, it's going to be a pain to find a suitable replacement.
ch_scr is suggesting I try a PN4118A as substitute but, if I read the datasheet for it correctly, the ON resistance is in the kOhms, while the ON resistance for the WN1001 in the same region is in the low hundred Ohms.
Also, the 7150 is actually using PN4118A for TR7, while using WN1001 everywhere else, so I guess there was a reason for them to use different parts.
I will provide an update once I've received and installed the replacement parts.