Good questions that I've been pondering as well. On one hand, having the slot full means that it's been accounted for in your retroactive plan: Picking something up that requires a memory slot implies you went in with it empty, so it's a limit on your retroactive preparation. As a GM, I'd allow the drop or exchange you propose simply because it's the most intuitive way for me to look at it: You freed up the memory by dropping/giving/exchanging an item to allow you to carry another.
It seems to me the best way to mark it on your sheet is that the row of 4-6 memory represents how much of your load has been accounted for, while the marked slots on the equipment and Coin sections can be freely swapped out, so long as the total doesn't exceed the number of marked memory cards. As long as you have unmarked memory cards, you can do flashbacks to say you brought along whatever equipment.
One thing I'm considering is a mid-score refresh of memory in the form of a rendezvous with a supply vehicle or something. Then again, the whole thing is also complicated by using the slots for indulging personal recall, which is something not quite so easily dropped off, at least in my mind.