It looks like JAL, Korean and Air Busan are the only ones with direct flights. The KE flight is a codeshare on JL metal. It looks like Air Busan also does some codesharing with Asiana as well. If you are going to be doing this flight every week I would imagine that going direct is the best bet.

I am not especially familiar with either program. Depending on your booking class though you have options to credit with alliance partners. So, if you are flying JAL you could credit to your Avios account. Or you could credit to AA. But I would look into the benefits of JL's program to see what kind of elite status requirements and benefits they have.