I keep all my furniture in the bank. In fact that's all I have in the bank except for some alchemy and provisioning items for lazy writ crafter. Anything else I keep fits into my housing storage chests.
Okay a furnishing bag isn't possible, why not add more 'housing storage' coffers? Add one that's like 120 slots instead of 60 but you can only put furniture in it. Give me 4 of those for 2k crowns each and I'll at least put a dent in the amount of bank space I have to dedicate to furnishings. That or make it so you can retrieve any furnishing from any house so I don't need to remember which of my 700 slot garages I put those dwemer pipes.