My initial thoughts is to spiral climb on the west side of the mountains to 11500 MSL then skirt the north side of R-5103C as to avoid it and also avoid the high peaks north.
Any good suggestions? I’m planning to do it in early November and I can fly in the early morning to avoid high DA.
So why not just file and be done with it? Or do they usually send you all over the place down there?
If you want to go VFR, just call 1-800-WXBRIEF (800-992-7433) before your flight and get either a Full or Abbreviated briefing and ask specifically about the Restricted Airspace you want to fly through. They should have relatively up to date info on the R Airspace.
When you do depart, contact Holloman Departure on 128.1 for Flight Following and confirm what, if anything, is active. If nothing is active, I'd just climb going south and then turn when you're high enough. If you can't go through R-5103C, then climb over the airport until you can start heading Direct. It looks like you can cut just south of the mountain peak at 9.5 and you're clear at 11.5.
If you happen to have ForeFlight and have the Essential or Premium subscription (I'm guessing you would if you're IR), be sure to check out the Hazzard Layer in the App to help you pick your altitude to clear the mountains. Same with anything in the panel that shows you terrain, go ahead and turn it on if you've not flown over the mountains yet. In this case you're close to the mountains, but sometimes if you're a ways away from the peaks it is hard to tell if you're going to clear when you get there.
Oh, and others have said, I wouldn't worry too much about the climb. The 182 has good climb power and you said it would be in Nov, not Aug. And if going up that high is not what you're use to, do read up on leaning. I do not remember which way for the 182, but you may be able to... are supposed to... lean in the climb. I don't in my plane, but you may be able to in yours to get more climb power. So DO read up on it or check with your mechanic, etc.
