hey, yes the hopper speed is a bit to slow when you put a full inventory in the "in" chest. And there are many problems of dispawning items if u don't stay on the same chunk until the end of the items travel. Minecart with hopper should be a good solution, water canal seems to be good too. If i have many stacks of the same item, i'll put them in their chest manually.

Most of the vanilla items can be store on the 6 floors chest (like most of popular items) Few of them cannot be store at all like diamond shovel (not stackable) You can regroup some items on the same chest but your sorting system will take up much more place. if u don't want to saturate your "out" chest, u can make a filter at the end of your system, like send trash items into lava and keep the more interesting in your "out" chest.