Hi we have a similar problem with one of our horse. We have an 8 years old akhal-teke×throughbred mare, she works quietly well, does rounds, circles, flexion, anything you want on bit. She jumps 1.90 and my husband showjumps with her. But after 4 or 5 jumps, she begins t get faster and faster, and pulls your hand with more and more weight, even about a weight of 90 kilograms. That's why I cannot really ride on her, only my husband is strong enough to stop her with full of his strenght. It feels like you are trying to stop a scudding railway.
Usual riding faults are excluded (not enogh safe hands, etc...), my husband does it for 20 years and no other horses showed this problem so much. All of our former pulling horses could be dealt with some usual methods (flexing, making circles, using softer or harder bits, going back to basics. Etc.). And the other hand this mare NEVER refuses doing anything, she does lateral trotting (I don't know if its the right expression), never stoppes before jump, never evades obstacles. When she begins to pull and run she's still directable a bit, but circles does not slow her because of her extremly good balance - she dares to do small circles with an extreme speed.
I would ask you if any of you has some experinece about similar horses, even akhal-tekes. Thanks.