I have two problems to solve and hopefully this can be done with a single (dual) part.
1. Supply a "clean" -15 V at about 35ma to a transimpedance amplifier from a -38V source,
2. Provide a steady-state -38V and (2) a timed sweep from 0V to around -5V. Here, nanoamperes of current are involved.
I considered an LDO for -15, but those I can find won't take the -38V presently coming from a converter and we don't want to create another noisy switching converter!
So I'm thinking a "high output current" amplifier (dual package) powered by our available -38V (with the + rail of the amplifier to system ground) would be an option. One of these would produce the -15V based on bias at the inverting input, and the other driving the -38V rail with a mosfet-selected triangle generator for the timed sweep.
Does Analog Devices have a suitable part for this idea.. or other ideas that will give us these voltages?
Those are two interesting problems. There are a few high voltage opamps to take a look at but I suspect none of them meet your needs for one reason or another. Harry's recommendation is probably the best: ADA4700-1: Single 100V precision opamp. However,35mA would be pushing the output drive capability of the ADA4700-1 close to its limits. ADA4700-1 wouldn't work for your second requirement since is not a rail-to-rail output. I'm not sure what you mean when you say provide a steady -38V and a timed sweep from 0V to -5V. Those seem mutually exclusive.
All in all, I still think you're better off with a switcher and an LDO. I might suggest the ADP5071 and ADP7182. What generates the -38V. Does the -38V have a lot of variability or just switching noise?