Something like the system Obsidian mentioned for their Project Eternity (a small number of alternate equipment slots, for items that the character can switch between on the fly; a limited pack, with items the character can access at any time outside of battle; and a stash, unlimited storage space that items can be instantly sent to while adventuring but which can only be accessed to retrieve items at inns or player's house/stronghold) would work quite well I'll say, though now that they said it I don't think it can be used by others, definitely not with a somewhat similar target release date. But maybe it could be worked out slightly differently yet still along the same lines? That'd allow you to still add limits if you want them without forcing players to discard items or backtrack like mad to whatever stash they decided to create for themselves.
As for the tetris effect, I go with a simple weight and bulk thing. Item X has weight Y and bulk Z, also a numeric value, and the pack can hold weight X and bulk Z, when an item would cause either total to exceed the maximum, it can't be stored there anymore.