Video?
UFP has a lot of different types of presentation… but… the symptoms you’ve mentioned are not unusual for UPF - how does the vet know it isn’t UFP? I’ve seen UFP present during either phase of limb movement (stance + swing).
Were the stifle issues there before, and the vet was thinking that injection of the hocks would help? It could be possible the stifles are aggravated because the hocks were sore prior to injections – however, usually sore hocks are secondary and not the other way around.
I wouldn’t be doing any other injections until you have x-rays/ultrasounds. There really are a lot of different things that could aggravate a stifle, and injections are only the answer sometimes - but I’ve found not always. Sometimes the stifle can be a red herring for other things, like cervical arthritis (which fits the symptoms you’ve listed) or SI disease (doesn’t really) in which injections would be a waste of money.
Toe-dragging with catching would make me leap to UFP immediately. Barring that, some sort of stifle lesion could cause the dragging and the clunking, but I would think it would be quite consistent - they are usually fairly lame when a lesion is involved. Other out of the box things would be suspensories (toe drag + stiff downhill) or c-spine arthritis (which fits all of the symptoms above).
To give you two recent examples:
When Boo had his medial tear in his stifle, he was very lame - 3/5 - weight bearing, but very quick and snappy. He never slipped or caught behind, but he was lame and would drag the toe along the ground and keep the leg out behind him as long as he could before landing on it. It was extremely evident.
Another gelding of ours slips and catches his stifle most often at the walk when he is first asked to collect, sometimes at the trot and never at the canter. Was not lame. At first we thought weak stifles and we chiro’d and put on two months estrone with no improvement. Some other stuff happened, that made us think of his neck: x-rayed his neck and he had some pretty significant remodeling. Injected his neck + the slipping went away for about 8 months. He’ll have to have his neck injected/maintained routinely the rest of his life, I think. He’s10.