I think the OP is talking about intercontinental, e.g. TATL/TPAC travel. On the reconfigured 744/763s, upgrades can even be tough for 1Ks. But, there are two great possibilities as a 1P/2P using miles:

A. Book as close to 330 days in advance as possible if you're on a reconfigured route.
B. Fly on 777s. Tons of NC space on most 777 routes for any day you want.

My parents have been 1P/2P for years (with MP visa) and haven't flown transcontinental in Y for at least the last 5 years (with at least one trip every year).