Welcome to FT!

If you are chasing the lowest fates and flying so little, it may be a moot point.

Suggest you check into alternative ways to collect points with FB and as lomg as it's not costing too much more, fly with a ST carrier. On long haul flights my cut point is $100-150 more to fly on a OW carrier. That is a purely subjective number and YMMV.

Beware of fares that don't give full credit, or perhaps partial credit.

Depending who you fly with, Alaska Airlines might be an interesting option for you. They have some partners that may allow you to collect some miles based on the limited information you provided.