I started her myself, so I know everything about her.
I've done what you described, and when I try to lope, she's just bunched up like a spring.
She's fine W/T. Heres a video working barrels from today:
Her stop is almost 100% body cues most of the time (takes a few practice stops to get it working) so she is not ignorant of MY position.
Once I start to lope her, she bunches up like a spring that you've squeezed between your hands and its a disaster. So, that's why I think letting her go would be a good idea. I never just let her go though, sometimes she wants to trot before I've asked for it, or wants to lope before I've asked and I will take her down a notch and maybe even stop and back-up before carrying on.
So, if I decide to run her, it would be at my control that she'd get up to a gallop, not her choice.