Using L2 to save on gas when “just moving some assets around” on L1?

Vague? Sorry.

I have an ENS name, a few cryptokitties, and a mishmash of other stuff that I would like to transfer from address A on the main chain to address B also on the main chain.

I guess I could permanently move them to some side chain. There are a few that look like they'll be around for a while. Maybe moving L1->L1 is the wrong move. I could be dissuaded.

I have an MM wallet that I never really trusted to begin with and now a hardware wallet into which I'd like to move everything.

I could get started on this and "just see", but suspect I could easily pay a bunch of gas just to get myself stuck in a corner, which in order to escape I need to spend MORE gas. Going to/from L1 inevitably costs "real money", the efficiency gains only realized after moving over to L2…

Of course the root goal is just to save on gas. I may be looking entirely in the wrong direction.

l'il help?