I would go with bias binding .... the stretch it allows you will help turn those inside corners, and help lessen the cursing of the inside corners!
Let Best Press or even a starch, be your best friend to make the bias binding.
Treat and press it well, before you start cutting, to help control any stretch-risk!
Then make your binding, as you normally would.
That's the easy part .... then the fun (???) of the inside corners.
Good Luck!! ... I am sure you will do fine.