Regardless of how you end up choosing to secure your crate to the rack, it will always make your bike top heavy and prone to toppling if you don't keep a hand on it while un/load the bag from the crate.

Honestly, for your application, I'd probably look into mounting some DIY hard-sided panniers (kitty litter buckets, small tool boxes, dry boxes, or even ammo boxes) and then strap your bag down across both of them.