I (used to) use small plastic stackable trays for this, (the clear plastic trays from individually wrapped cheese slices), with all of the screws from one stage of disassembly in each tray. Then, when reassembling, I'd just work back down through the trays.And draw a layout of all the screws you can see and as you remove them, place them on your drawing so you know where they go and don't get confused if some are longer / shorter.
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