Personally I float for 30 minutes, then just scoop and pour water from the bag/cup until I'm pretty sure its just water from my tank. Better than dropping them in at once and shocking them.
I don't like drip, and if I do its less of a drip and more 'who didn't turn off the sink completely' line speeding it up. IMO its more dangerous to leave them in their filth water and ammonia/PH can do some funky stuff when the oxygen suddenly changes. That's usually what causes ammonia poisoning.
If its something that doesn't stress and produce a lot of ammonia (echinoderms, coral, anemones, etc) then there's not much harm in doing the slow method except for PH.
Everyone has their own method that works, personally whatever method I try/practice I never run into problems either way, except for arrow crabs idk I'm cursed when it comes to arrow crabs, 2/3 died instantly when touching the water and one of them I was just transferring from a different tank.