God... THIS...
Do you know how much time I waste managing inventory after a 4 hour stint? Yeah, I'm a packrat. I'm a looter. I'll sit in a new area and canvas it over 5 times looking for boxes and containers I might have missed.
At came, I got my bag of magic items, bag of potions, bag of clothing, bag of shinys, bag of scrolls, bag of oddball junk, bag of alchemical junk, bag of camp supplies, bag of books...
Do you know how long it takes to go over all my characters and manage it all without a "box-select"? Or weed out duplicates or make stacks without auto-stacking or sort by NAME? Or have to run around and drop/add characters just to find that thing I'm looking for that I forgot to remove from them before I swapped them out?
Typically... an HOUR. An hour of item management! It's crazy!
Here's an alternative suggestion...
Keep the system you have now... BUT... when you remove/add a character, all their inventory is transferred to the new character except their equipped items. No UI tweaks that way, but, that said, OP's suggestion is a far better, more comprehensive solution.
Additionally... Maybe, while in camp... have a quick-button to open the "Traveler's Chest" inventory... and allow the inventory grids to be resized horizontally as well as vertically. Add some "filter" options and a few more "sort" options (like name). Double-clicking a bag in a chest should ALWAYS OPEN it... NOT transfer it to your inventory.