Can’t speak to this question specifically- but I do know that at MK - when I had multiple popcorn buckets and they didn’t have a locker available- they stored them in their ‘virtual’ locker (basically space where they keep wheelchairs, ECVs etc) for the same price as a large locker.
Keep in mind that while EP and MK offer the Jumbo sized lockers, park entry rules have a smaller limitation of 24′′×15′′×18′′.
It might seem like a contradiction that the jumbo locker allows larger than park entry rules, but that is because people with multiple items might still find use for the jumbo locker.
Luggage is not allowed on Disney transportation how were you planning to get to the parks? If MK is the park you are visiting I don't know how you would do this unless you took a MinnieVan although that is also technically Disney transportation.
Suitcases, bags, coolers or backpacks, with or without wheels, larger than 24" long x 15" wide x 18" high (61 cm x 38 cm x 46 cm) are not allowed in any theme park or water park. Loose or dry ice is not permitted in these containers. Re-usable ice packs are recommended.
If your bag meets the restrictions, you would still be subject to security screening, and you will likely get flagged to go through your bag to make sure you don’t have any prohibited items.