If a short spurt of moving mechanics was coming up, ones which prevent Iaijutsu casting... couldn't you just... Hikaze + Jinpu/Shifu to prep for a new Sen and then Midare + Tsubame after that window cleared? It isn't the most immaculate answer to the problem, but it could buy 4-5 seconds of minimal interruption instead of 4-5 seconds of total DPS outage.

Also, there is the ability to start casting and then move over the last X% of the cast bar... BLMs and healers know what I'm talking about. You could always game that soft spot in the code.

And if the mechanics are so intense for an extended period of time, you're most likely not in melee anyways.

Truly, though, adjusting to these sorts of challenges is what like... everyone has to do in some form or another.