What you're saying is exactly what my understanding is from USEF rules.
But breed show hunter pleasure and under saddle can be wildly different, and judged by a completely different standard.
Here's an Arabian Hunter Pleasure class -
Note the horses being ridden on contact and with a lot of head set, some behind the vertical, and the knee action and animation.
And here's an Arabian hunter under saddle - Moon Dancer - Arabian Horse Hunter Under Saddle - YouTube
This is why I really, really hestitate to give any advice about breed show hunter classes; they are just a horse of a different color!