I faced this situation not that long ago myself, personally I feel like my Experience worked against me as the School appeared to be looking for Instructors with no "Bad Habits" garnered from GA.
I can't say I entirely blame them but it sure was a kick to the guy and I feel that the Bigger schools care less about your past experience as they're more focused on strictly following SOPs and Standardisation which they feel can be compromised by more experienced Pilots who will teach the SOP and then show them "The way you'll actually do it". Once again, I can't blame them, it's a perfectly valid way of doing it (The best way?) but then I feel it really defeats the purpose of having experience except for the confidence it gives your Students at the beginning.
Personally I'd recommend aiming for the Smaller Schools, they'll likely be more appreciative of your experience and allow you the ability to change things up a bit more to suit your Student and your own Experience.