While onboard, I store mine on my head
As a kid, my Dad's policy was no riding for a month if he even saw me swing a leg over a bike without a helmet on. I've never been able to shake the habit.
When stopped, I either use the stock helmet lock or carry it inside with me. I always have too much crap in the saddlebags.
Have you tried laying them on their side?
I wear a lrg or ex-lrg depending on brand, and I have had better luck fitting my plus sized lid in my saddle bag by placing it bottom down on the door of my bag and then closing it (with a small towel in the bottom of my bag to prevent scratching. The helmet ends up on it's side.