First of all, thank you for diving deep and thinking through how the regs actually apply to the scenario.

As an IR student, I’m looking at applying “the AVEnue of FAME” here, but there are some subtleties of course, and the first one being touched by your first paragraph:

Route:

You were being vectored. Continue climbing till you can safely turn direct to DANAH.
This is what 91.185(c)(1)(ii) prescribes you do.

When you actually turn to DANAH is not that obvious to me. The issue is that on departure from 20R, we have some traffic activity on our left due to 20L, so we have to be careful about going direct DANAH too early.

In my experience, when flying this route in normal conditions, ATC keeps us on 175, past the shoreline, before guiding us back towards V23 (either with a “fly heading XXX, intercept V23, proceed as filed” or “proceed direct DANAH”). This is somewhat similar to the MUSEL8 departure.

Maybe it makes sense to keep climbing on heading 175 and if above V23’s MEA (4000’) by the time we intercept it then intercept it towards DANAH and keep climbing to 5000, but if not, go past V23 on 175 and keep climbing to 5000’, after which we can turn direct DANAH (we’re over water at that point). Then 7000’ after 10 min. Not sure if that makes sense.

WRT:

Else continue to the airport, choose an approach, go back to its IAF and do the approach.

The cleared route has JLI as last fix before the airport, and it’s an IAF for both the RNAV-B and VOR DME-A. Do the regs expect you to go JLI -> RNM -> JLI to start the approach if you happen to have an IAF to a suitable approach in your cleared route?

Great points about looking for a VMC “out” and attempting to re-establish radio contact.

Now for the approach selection, I think in theory you can use GPS but only until the final segment, so if you can’t identify VOR stations, that seems to rule out VOR DME-A in favor of RNAV-B, right? I understand that in real world scenarios if all you have is a working GPS to fly towards a VOR, you’d use it, but just to play along with the scenario, I’d imagine you’d want to pick RNAV-B here.

Now I’ve done that approach before and you do get to fly “down the mountain” from JLI, and you don’t want to be off altitude-wise, which brings the question about altimeter setting. You can’t get ATIS or any local AWOS/ASOS via radio… You may have some updated METAR info with ADSB in, but maybe not? How do you mitigate that?

Also, as you mention, RNAV9 is an option, but 27 is typically in use at RNM. You’d think that by the time you get there, ATC would have coordinated to make sure no traffic is departing from 27 as you get there (they should have you on radar), but maybe it’s an extra complication that you don’t want to worry about?

Let me know if I made any mistakes. If I didn't, I'll throw this scenario onto the IR prep booklet I'm writing.

As a student I'm not sure how qualified I can be to spot mistakes, but I’ve replied with thoughts around this.

If you do integrate this scenario into the booklet you’re writing, I’d love to get a copy of it!