I was in the same boat as you concerning sheep. Last year the sheep hunting gods smiled upon me and I drew a NR tag in Oregon, pure luck as there are no preference points there for sheep. I put a fair bit of effort into scouting and killed a nice ram opening day. To be honest, the hunt itself wasn't particularly demanding, but incredibly rewarding, definitely the highlight of my hunting career!
Anyway, if I were in your shoes, I'd keep applying for tags here in the lower 48 but start saving for a guided hunt in AK or Canada. Goats are less expensive than sheep from what I understand so you might start there. You say you hunt elk out of state in 2 states. That's a fair chunk of change you could be putting towards a sheep/goat hunt. By prioritizing your wants, saving the money shouldn't be too difficult. Another option for a mountain hunt without spending your entire retirement savings would be a tahr/chamois hunt in New Zealand.
You can't win if you don't play... Good luck!
