Typically I split my deck in half then shuffle each half deck multiple times before then blending the half decks back together.
i do the same - multiple smaller stacks. My stack is extremely tall because it's thick-sleeved, so i play with it in a horizontal orientation using homemade card holders like the ones seen here:
(That photo was taken before i managed to get a copy of the Footlocker, so the stack seen there is quite small.)
I’ve thought about using an automatic card shuffler but I don’t want to risk damaging the cards.
i looked into these a couple years ago but didn't find any which claim to support sleeved cards.