First, what a LOVELY mare! I’m sorry to hear she’s injured, hopefully this is just a temporary setback?
Her back isn’t long at all
Do you have any pics of her feet? “terrible” is pretty subjective
That said, if her feet are really genetically that bad, you might find you can’t improve them a ton, so decide if a little improvement is good enough.
Even seeing this picture, it’s not “very long”. Many would say it’s a great length for a mare to carry a foal. I think too many people have gotten used to the more recent (it’s been a while, I think it’s slowly trending away) trend of pretty short backs, breeding for “tall rectangles”. Your mare is much more square, to maybe approaching a slightly long rectangle
Leg-wise, she’s a bit camped out behind, but nothing that makes me cringe. Her front legs are a bit light-boned even for a TB, and a bit tie-in. You just want a really correct-legged stallion.
I even hesitated saying “light boned” because in general, TBs ARE lighter-boned relative to their size than many other breeds, but what most forget is that they have been bred for a very long time for bone density. There’s just more to bone integrity than cannon circumference
I have no input on stallion ideas, that’s taken care of by others, I just wanted to add those things about her confo