There are extra jumbo sized lockers *outside* the bag check area, on the DTD side, in the picnic area. It's *possible* a carseat would fit into one; they sure were enormous when I just had carryon sized bags to fit into a Jumbo!
But if they don't fit, then what are you going to do?
Have you looked at ART to see if that would get you there pre-MM?
No one is allowed to lock anything to anything in the parks. If a CM finds it, they will get lockcutters and take care of it. There are people who use bike locks to lock wheels to wheels, so that only the front wheels can be used to push a stroller along...a CM can still use it to move if needed, but it would be really awkward if a thief took it. But don't lock a stroller or a carseat to anything...just imagine what it would look like if you came across a carseat locked to something? "Hello, security?"