Ship 1 must be special or something, because I've never run into any of these problems in all my time with the game thus far.
If I join a beacon on the ground, I never run into any issues with being able to loot before the PL restarts the quest (when applicable), and when I run a party, I'll usually swap lead to someone else that's in my group after I'm done grabbing my EX-cube fodder before leaving the group.
To be fair as well, most of the loot in PSO2 isn't really worth anything to begin with. You should have materials, 13* Weapons, and 12* units set to auto-pick up from the get go, and any weapons drops that you may get from a UQ boss with potential augments on them shouldn't take you more than a few seconds to scoop up once the crystal's been broken, doubly so if you're going into an UQ with a maxed out inventory, or even a standard inventory that's not filled with crap you don't need, especially since most UQ's now are one and done.
I mean, if you don't want to join a party for an XP UQ like Halloween, or a 12-man UQ, that's fine..But for the love of all that is holy, if you're going to pug one of the 4-man rematch UQ's, there is zero reason not to join the party, and in fact you're just making it more difficult for everyone else if you don't.