Sorry to butt in, but HITS, I know exactly where you're coming from - I show my horse as a hunter under saddle here in the UK, and whilst he has a lovely movement, his WB breeding has left him too tall, with too little bone and too boxy a body to fit into either lightweight hunter or riding horse/hack classes here. I still show him because we both enjoy it - he doesn't tend to place unless the judge is riding, and then he gives a very lovely ride so tends to do better. I can't change what he looks like, but I have trained him to take any kind of rider, to be light in the mouth and to carry himself in an outline without being prompted, which a judge appreciates if he rides. Basically, have given Fitz as much help and training as can possibly move us up the rankings!!
For us, showing is a bit of fun, and something different from the eventing that is not only a good day out, but is not stressful or taxing in the same way as eventing is. We'll never win championships, but we enjoy ourselves, and we aim to get better every time.
I see what you mean about Sandie's movement - I'm no American Hunter rider, but I know a bit about judging horses' movements from our showing here, and you can most definitely train to improve her movement if you want to. You say she likes a long, low outline - use that to lengthen her back and encourage her to round and engage, and get her hindquarters powering her more. Once she's more engaged, the collection into the smaller paces the APHA seems to want will be much easier. Long & low is a great way to build up self carriage too.
Best of luck, and don't let the craziness of the showing world get to you. I've seen not only completely lame horses get pulled in first, but perfectly sound only on the forehand horses dismounted as lame - the judge calls it, and unfortunately not every judge is the same (or even sane).