Now I've emptied tons of random stuff out of some of my chests in my home. So where can I find a respawning chest to dispose of some of it? Can I use that invisible chest up in Dawnstar?
Most chests, containers, corpses, etc. will respawn after awhile. You
could use the Dawnstar chest, but it's not necessary. Sell unneeded items to vendors or store them in the countless chests scattered around Skyrim as you come across them. I would also advise that you pick up
every single weapon fallen enemies have and store them either in their corpse or a nearby chest/container. It's quite tedious, but it should help prevent your save file from getting bloated because once your save gets to about 20mb, you will experience a lot of lag.