But I have gotten myself in trouble by using the phrase, "Good girl!" because if I'm on her and she gives me a trot when I ask for it, "Good girl" pops out of my mouth without even thinking, and she stops for a treat
If "Good girl" is your secondary reinforcer, then stopping is unfortunately the proper response. The secondary reinforcer is a terminating signal and the horse is correct in waiting for the primary reinforcer.
It is actually a very common problem of trainers who do not employ a proper reinforcment plan. They use their "clicker words" ambiguously, sometimes as secondary reinforcer (often means horse can stop afterwards and is petted), sometimes the same word is meant as bridging signal though. That leads to grotesque scenarios where the trainer has to use code language with the student to circumvent the accidentlly established "clicker words".
I would suggest, as Donald already hinted at, the best way to solve this problem is to establish a concise clicker word/sound.
If you load that clicker sound prior to every session for a while, I'm sure that the terminating meaning of "Good girl" will soon fade out and you can introduce it as a handy bridging signal
A clicker sound is easy, as the chance to use it accidentally is minimal. When using a word, just choose carefully. I use "Bravo", as it is a word I usually don't use in training and other people don't use it as well. So far it works fine.