Sounds like you're going to want a program with a long validity period. Asiana would be an easy way to get *G status since they have a 2 year qualification and they also have a 10 year expiry on the miles, so you have a good amount of time to use them on something. Having said that, you'll earn quite a lot of miles in United Mileage Plus because of the airlines you're flying, LO is pretty standard for earnings, but LH, LX, OS, and AC all credit really nicely to UA Mileage Plus when you're flying paid J. The only downside is you can not earn status if you don't fly United at all, it requires 4 segments a year on UA Metal. UA miles don't expire if you stay active at least once per 18 months, either earning or spending.
Those are the two programs I'd be looking at the most in your situation, depends on what you want to prioritize more, earning miles or gaining status. (Or alter your patterns and take one round trip with a connection on UA per year to get the 4 segments necessary for status.)