Have you considered New Zealand? You can go roundtrip in economy class for 80k per person with a free stopover in Fiji on their partner Fiji Airways. You'd need to leave from LAX, but that's manageable. Just buy the extra 10k miles needed (Alaska is currently running a mileage sale), but only after you find inventory that you actually want to book.

While some folks may chafe at the idea of flying in international economy class with miles, Fiji's business class is nothing to write home about and it's very difficult to book. If you add a Fiji stopover, this would be a really expensive cash flight.

Bonus: Want to take another trip anywhere else Alaska flies? On the way back, make your stopover LAX (for up to 11 months) and continue your journey onward to, say, Hawaii.