Good news! :) The vet says it's not arthritis!
She watched him move in a round pen and observed that his left leg's movement was not as "animated," most obvious at the walk and jog (but less so at the working and extended trot). I showed her the odd way he lifts his foot when asked and she determined that it was likely a stifle issue. Fun fact! The vet said that typically for an issue in the stifle joint, a horse will slowly lower the leg and even hesitate (as opposed to slamming it down, which might indicate an issue in the hock). You learn something new every day!
She did flexion tests on both of the hind legs and no arthritis was indicated. Rather, she's thinking the issue is in the patellar ligaments-- not upward fixation, but some "loosening" that he is compensating for. Jax was horribly out of shape when he came to me 7 months ago, so I think this diagnosis is actually pretty reasonable, since the symptom has improved with his fitness level thus far. Luckily, the recommended treatment is lots of conditioning and exercise up and down hills, and she sees no reason why we shouldn't move forward with our dressage training!
We are doing a bute trial later this week to determine whether he is in any pain-- although Jax is typically the kind of horse who lets you know, haha! The vet described Jax's lameness as most likely to be a functional lameness (where the lameness was an adaptation in his movement, as opposed to a response to ongoing pain). Fingers crossed it is indeed functional and not painful!