One thing that hasn’t been brought up is how balanced and consistent a rider the owner of this pony is. It could easily be contributing to the time it is taking and what, to me, appears to be a minor occasional buck.
When my, now grown, children started with their pony he would buck occasionally when they tried to get him to canter. Canter was actually his favorite gait (over trot). He knew how to canter but was still green in many ways as a 5 year old. If he felt like he was loosing his balance or the kid up top was not sitting balanced enough to suit him, he let out the occasional buck, but always kept himself underneath his rider. It was never a buck to unseat them, it appeared to be much more a buck to say “hey, let me toss you back where you belong.”
Like the OP’s pony, he was super round with NO withers to hold a saddle in place. You absolutely had to ride well balanced to keep the saddle from shifting to one side or the other no matter how tight the girth was. That may be the case with OP’s pony too.
Our initially green pony turned out to a saint with a great sense of humor, loves people, is basically bomb proof when it comes to all the handling - clipping, loading, vet, farrier-, and to this day still loves having a job. He took both my kids to many local low level show championships and even made it into the ribbons at the state level in 4-H. He taught my kids a ton about both riding and life.
I would not be so quick to write her off just because of an occasional buck. It may well not be pain related (although I would have it checked out to be sure). Much of the rest of what has been said would make me consider OP’s pony as a decent prospect for an ambitious 4-H kid with good supervision and guidance. Personally I might value her in the mid 4 figures+. I would not even rule out paying the 7K+ mentioned up thread if she is a bit more finished. At her age, she is mature and solid enough to be past the young horse antics stage, but could still have a decent number of useful years in her. You can always come down on the price if she is not selling. If you continue to work with her until she sells, she may surprise everyone with what she has to offer and what she is worth.
Our pony is coming up to 30 years old in a few weeks and now he and I still amble round now and then. His best fun is having my son and 2 year old grandson hop on for a pony ride together. Who would have know what a somewhat rough around the edges, green, 5 year old pony would turn into. Surely ours is not the only saint out here. This gal may be another. Best of luck with her.