I think the set is good for something like the Battle Tree if supported well, but it might have more trouble in competitive formats like VGC or Smogon Doubles. You’re completely right about the speed, and although it’s outclassed as a Swift Swimmer, I think that’s still probably the best way to use it given the naturally faster threats it faces. Z-Hypnosis is really cool, but the two big problems I see with it are the terrible accuracy of the move itself (plus you won’t need the speed boost as much in the rain with Swift Swim), and the extremely common terrains of Tapu Koko and Tapu Fini blocking sleep. It can still be used against Zapdos, Lando-T, etc., but many of those threats give you other trouble, and you’re still risking the accuracy. For those reasons, I would suggest Waterium Z, as a rain-boosted Hydro Vortex can be very strong, or maybe even the fighting z move for Focus Punch (or Dynamicpunch?), though the fighting-type moves are potentially useless after using the z move.
So I think your spread is fine, and Adamant is ok if you go Swift Swim, but Jolly may be necessary if you keep Water Absorb. Protect is necessary for the last moveslot for competitive douibles (though you can probably get away without it in the Battle Tree or casual battles). I think Waterfall is a no-brainer, and then the remaining 2-3 moveslots (depending what you do with Hypnosis) can be filled by a fighting move, Ice Punch, Rock Slide, or Poison Jab, depending what coverage the team needs. I’m not sure Poliwrath has enough bulk/reliable recovery to have time to set up Bulk Up, but it could be worth a try!
Getting rain up shouldn’t be too much of a “hassle” with Poitoed (who has great support moves like Icy Wind and Helping Hand to boost a Hydro Vortex or something like that even more) or Pelipper, and there’s decent ways to set it up manually. If you stick with Water Absorb, I do think that Surf (Muddy Water does not hit a teammate) somewhere else on the team could be ok, but you really need a way to reliably handle things like Kartana and Tapu Koko for Poliwrath then.