AFAIK Depending on who you ask, the washing is/isn’t maakev. My Rav, a descendant of the Rambam says it’s not meekev, which I believe is the shita of the Rambam. When I take a long time to daven and have little time to wash, I don’t wash as per his instructions. He wants me to go up immediately at Ritseh. The first Mishna alludes to that. The Kohanim go in immediately at Tsait to eat their terumah.
As far as the bracha working better, that’s not our cheshbon. We have to do our hishtadlut the best we can. Hashem will do the rest.