I assume Katie doesn't have the collar anymore...yay!
My girl has one on now as she was just spayed and I had to figure out something too.
In case you ever need to use one in the future....of course the collar falls off as their had is smaller than their neck. I really don't even understand what anyone putting it on a greyhound thinks....why would it not come right off?
So, I've made a harness type of loop by tying one end of a bandage wrapper onto one of the loops (of the collar) and then put the wrapper under her armpits and on the other side brought it back up and tied the other end to another loop of the collar.
This has worked amazingly, as you can imagine, as the "harness" keeps the collar on. And she's also way more comfortable. The harness is comfy on her....doens't restrict her movement and is soft and wide (unlike a piece of gauze would be) and MOST importantly, it's safe!...as she can't push the cone off her head in a millisecond like she did before.
Whew...problem solved.