I know it won't fix things, but here are some suggestions for addressing some of the BtC gear that is keeping TR Caches filled to the gills:
In ESO, they have a sticker book system. It's a UI that you can use to track your collection of gear you've looted over the years on all your characters. You can craft these items using a crafting system in that game. The more gear from a zone or dungeon you've collected makes the costs of crafting the items, for that zone or dungeon, cheaper. The nice thing is, players don't have to hoard as many items in the game, as they can just craft those items after they've collected them even just once.
Another idea is to just make a lot of the BtC items in, at least, the older content of the game, BtA. Say like pre-Ravenloft xpack, or pre-Sharn or something; "anything over 5 years old" perhaps. This would allow the movement of items by the same player on the same account, but not flood the server with items that are behind pay-walls or harder to get, or only raid accessible. It certainly would have helped in this situation, as from what I'm reading most players commenting here have several toons that are over capacity in their TR Caches. Meanwhile we've just been given 100 Shared Bank Slots (and are about to be given about 800+ inventory and character bank slots for free with the +10 Character Slots). I think 900 Slots would cover a lot of the TR Cache problems we're facing, as long as the items weren't BtC. I'm not suggesting using Wishes of Inheritence, as was suggested earlier. As those are highly valuable, and costly items on the DDO Store. But, I am suggesting that a lot of older gear could be recoded from BtC to BtA, or in some cases even become not Bound at all.
The former suggestion would take months for them to code and implement. I imagine the latter suggestion could be done in a few weeks, or even less. Either way, it probably won't be useful at this point to fix the current issue. But, it's something that SSG should think about.