A few comments:
You can also redeem Avios on Alaska if, say, you wanted to visit SEA and then fly to Hawaii. The Pacific NW (SEA and PDX) is a great place to visit -- wine, craft beer, flight museum, etc.
Skip HNL (Oahu) in favor of Maui (OGG), Kaui (ILL) or the big island (KOA). AA likely flies nonstop to at least OGG from LAX.
If you don't want to spend a week in one west coast city, consider driving from LA to San Francisco or even all the wy up to the NW. It's a beautiful drive.
Finally, consider doing one of your long hauls on CX instead of BA. You can't use the 241, but you will get to try a different carrier with a great product.