I just tried with the extra happiness per fulfilled need perk and I got a lower net happiness increase overall. Obviously I probably didn't do the minigame perfectly, but I also didn't do it perfectly with my other run, and I actually spent more time trying to optimize this one. Having the beer without cups perk allowed me to get 3 fully fulfilled DIKs while I only got 1 without it, so that made the increased percent happiness not enough to overcome the ability to just throw shit on the board. Plus, idk how important your party score is gonna be in the future since the game is keeping track of total score, but you're certainly not gonna have a better score with that perk.
You are right that eliminating trashcans could be counterintuitive if one (or more) of the DIKs want trashcans tho. In that case one of the happiness per need perks would probably be the better second perk because less trashcans isn't as much of a space saver as the cups one is anyway. The extra multiplier per DIK over 50% happiness perk will probably be good perk to pick next episode if you can get everyone over 50% tho.