Contact some more, there will always be some that do what you want.
I'm upgrading my CRI to FI part time at the moment - the vast majority of schools would prefer me to be full time (and really weren't interested in showing flexibility involving the fact I've already been an instructor for 12 years), but I did find one that was prepared to offer the flexibility I needed to fit around my busy full time job. The same will apply to you I'm sure.
G