My little memnonic for these two kanji was to look at their very bottom right corner.
If you hold your hands flat with your thumbs out, your left hand makes an L, like the bottom of 左, and your right hand makes the box corner of 右.
I hope that helps someone!
When I was a child, I wrote "右" on my right hand, "左" on my left hand. I memorized those letters in a few days before the letters disappeared.
It took me a second, but I definitely see what you mean now. Literally the bottom right of each symbol, I.e. The bottom right corner is closed by your right thumb and the bottom right corner is open with your left thumb. Thanks for the tip!
I remember left and right by politics (warning: these are left-slanted :p )
Right has the symbol for mouth in it because the right is all talk, no action. Left has the symbol for work in it because it represents the worker.
I remember hidari as someone saying Hilary wth a thick Japanese accent. Hilary Clinton being a left-leaning politician.
I remember migi because it looks like MG which sounds like a machine gun to me, and the right loves guns where I live.
I never have trouble with these directions now :)