Thank you for all the comments. I admire the helpful nature of this forum. You never scoff at assisting those with less experience.
I will attempt to answer all the questions and suggestions you came up with, in chronological order. I will snip the quotes as needed to reduce the length of this post.
You seem to be saying you are giving it ONLY 17V for a 15 volt output.
But a quick glance at the datasheet, seems to indicate it (LM723) needs a minimum of 3 volts (between the input and output). Datasheet says "Input-to-output voltage differential, VC – VO (min)3V (max)38V"
That could explain your drift problem.
Sorry, that was a typo. It it is definitely operated at 18V, plus a few hundred mV to raise it above the 3V minimum (I just measured it - it's 18.4V). So actually we're almost back to that dangerous 19V.
Hello,
a) a LM723 is not a LDO it needs minimum 3 V headroom between VIN and VOUT
so dependant on your unstabilized 19V it might be out of spec.
b) according to the data sheet the C52 capacitor is usually not at the VREF pin but at the IN+ pin.
a) See reply to post above this one. The LM723 is operated above 15V+3V. (17V was a typo)
b) You are very right! This actually brought to my attention that the suggested high-voltage regulation circuit does not even have a capacitor on REF nor IN+, see attachment.
Could this have damaged the reference circuit? Charging a 4.7uF cap might have drawn more current from the REF pin than it's comfortable with. (Open question to all readers. Input welcome.)1. Use an oscilloscope and make sure nothing is oscillating.
2. I am not sure what the 723 reference output will do with 4.7 microfarads directly attached to it but the application notes contraindicate that. When input power is lost, I suspect it may cause damage to the Darlington emitter follower buffering the reference through base-emitter breakdown. As shown in the application notes, connecting that capacitor between ground and the non-inverting input may be acceptable if there is at least 1 kilohm between the reference output and capacitor.
3. Using the wiper of the trim potentiometer in that way is potentially dangerous. Wipers normally fail open and if that happens, the output voltage will increase. The end of Linear Technology application note 42 discusses this.
4. Measure if the reference is drifting. Could you have imposter 723s?
1) Done and done. Everything's nice and stable. Noise is within spec.
2) You are the second one to point out that the 4.7uF cap could be an issue (see quote above this one). I am beginning to suspect it might be the cause.
3) Thanks for this tip! I did not know about it. Will definitely keep this failure mode in mind for future designs.
4) Already on it

What component is that?
What is the regulator powering?
Perhaps there's a way to design the circuit so it doesn't need an adjustable power supply.
Trimmers are generally avoided in modern electronics, because it normally works out more expensive than using closer tolerance components, in the first place and it reduces the reliability.
The regulator is powering the collector of a common base amplifier. Making the 15V adjustable was a bit of an overengineering error on my part. There are simpler ways to equalize the gain among units. My current wish is simply to get the 15V rails stable, and I'll gladly forgo adjustability at this point. Thank you for the input on the trimmer, I will try to steer clear of them in the future where possible.