Just bring the backpack. Getting a locker for the rides that require the locker takes a few minutes. It's not a big deal.
We've never done Universal before, and have been spoiled by Disney's carry everything you have with you on rides policy.
OK, now that I'm a bit more awake and am off my cell phone, let me answer more.
At Universal there are a handful of rides where you can't bring things on and those waistpacks you got will be the only thing you can bring (along with eyeglasses and a lanyard). And there are two or three rides where you can
only bring on eyeglasses and a lanyard. Everything else is just like Disney.
The rides where the 3-pronged waistpack, or a lanyard, are ALL that are allowed, have free lockers.
Getting the lockers can be backed up, but that just means a little wait. If you can keep your wits about you and head threw the throngs to the back of the locker area, you'll likely find a shorter wait, because everyone just waits at the obvious front of the locker area. (I cannot speak to FJ with this as we've never used the lockers there...DH can't yet ride so he just holds onto our stuff for us) There are multiple banks of lockers and each bank has its own screen system. If you can, send ONE person to get the locker so you're not taking up extra space (like everyone else is doing). Same when it's time to retrieve the items.
And remember that it's not THAT many rides where the locker will be needed. I would, and have, NEVER change the way I'm comfortable touring just to save maybe 15 minutes total throughout the day (or even if it was half an hour) in order to not use a locker for those rides. We always have at least 2 bags with us. Gotta carry the sunscreen, water, perhaps some protein bars, etc.
Now, about the sweaters...although I freeze at Disney when indoors that hasn't happened at Universal for me. Well, if I'm going during a December or February and it's freezing outside then I'm *wearing* the overclothes. But unlike at WDW where I freeze indoors, or DLR where once the sun goes down I'm cold (even if it was 90 degrees during the day), that hasn't happened for me at Uni.