I haven't tried it, but if I was going to I would run something (sticks maybe) through it, tying it into the surrounding cob.
As for 'filler' remember in the old Tudor houses (cob + cow manure, with lots of rocks, sticks and other
land debris thrown in as filler). They were thinking just like you...
So maybe don't work so hard, filling bags with straw and such, instead fill the cob with straw, sticks and other stuff willy nilly not clumped up together, which will help keep it uniformed.
The Maure made their cob stickier which helps hold all that stuff in place and keeps the cob from pulling away. So consider adding some manure
or poo-straw to help with your fillers.
Edit: Oh yea, and WELCOME To Permies, we'd love to see pictures of your build ♥