Not sure I entirely agree with this. To my understanding, when you are simply observing a horse at the trot, you cannot isolate front end or back end. You need to do flexion tests on a straight away and a circle (and possibly nerve blocks) to figure out precisely where it is at.
From the OP's video, I see the horse's head going UP when the front left and right hind are coming into contact with the ground, which would indicate the problem is in one of those two limbs.
While most problems end up being in the hind end, I don't see how you can say the problem is in the back end. Because the horse will have upward head movement for a front end problem too; it just depends which legs are striking the ground at the trot. Unless you are seeing something I am not.
Do you have a good lameness vet in your area? Honestly, that is where I would spend my money first. Your horse may still need a chiro adjustment (and it's never a bad idea to have them checked), but if you've only got so much money to spend, I'd spend it on the vet.
Sure you can! Have you ever watched a vet or lameness expert first evaluate a horse at the walk and trot? It gives them a visual of if the front or back end is involved. Then they isolate exactly where with other tests. And this horse has issues in the back. Even without the OP talkiing about hock problems, you can see it by the way he uses his hocks and the head bob. He's not dead lame, but that slight head bob which some people may not even see...is still there.