We just got back. On our first day, I had my three-prong fanny pack and one of those thin, packable backpacks, which I brought to put souvenirs in since I knew the kids would be getting wands and would want to take off their robes when it got hot. Well, after one day of paying for the big lockers and stuffing the backpack in and out of them, the backpack completely ripped along multiple seams, and I had to throw it away in the hotel room. From then on we only used the free lockers. The kids kept their wands in their robe wand pockets for rides that they could keep them, and we put them in the free lockers when needed. It was honestly a relief to not have to deal with the big backpack anymore.
I will add that we had a stroller where we kept bottles of water, but I never left souvenir bags under it because I didn't want them to get stolen. I found using the room key on my lanyard to be the easiest thing for the lockers. We didn't need the lockers our last time on Hagrid's, and we skipped past a lot of folks who were in there dealing with them. The lockers at Gringotts were by far the most crowded and unpleasant, every time.