Are you aiming for hunters or jumpers or eventing? Or dressage mainly, but want to be able to jump too? if you’re looking to improve ‘movement’, than your answer really matters, as ideal movement won’t be same through all the disciplines.
Are you looking for fresh only, or would you consider frozen?
“moderate size” varies wildly between individuals, and a lot depends on how big your mare is.
What’s her conformation like? What are you looking to improve there?
There are several nice R-line AHS stallions that pass on good ammie-friendly temperaments. Not sure if they’ll improve the hind end drive, but many have offspring successful in the H/J rings as well as in dressage.
Another option might be Widmark. He brings in the power of the W-line, but many of his kids are really excellent jumpers. I believe he was in the top 50 last year for USEF hunter sires. I have a Widmark mare that’s very brave and an excellent jumper, but definitely has a lot of power and drive. Sometimes too much. However, I don’t know much about her damline, so I can’t comment on what came from Widmark and what came from her mom.