The only bottleneck is these two bindings with 3% drop chance each, nothing else is important. The only way to raise your chances is to run more MCs every week. You will probably end up with mismatched pieces on different alts first, before you get both bindings dropped for a single character, but hey, it is what it is.
Highly doubtful that this kind of timegated 3% activity can be meaningfully quickened. Better prepare for a long journey!