My older one is quite narrow but never rode "extreme" with it.
Can see how you end up with a very flat thing that's annoying though.
Get some ppe or similar sheet plastic and make something?
This thing from Vaude? It's peak German rando! If the attachment is stable that could be quite good. Depending on other bags could be nice to have quick access.
I have one of the alpkit handlebar drybags.
Works nicely on a rack with the things for straps.
They also make that style with just one opening.