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In regards to your hamstring tendinitis theory, if you’re not experiencing symptoms at the sites of the tendons themselves, then I’d say probably not. However, that would be a potential condition that could develop as a result of your chronic stiffness if you were to continue training hard without resolving it.
I’m curious about your execution of the hamstring mobility stuff you’ve been doing. Just to rule out the obvious, are you certain you’re not giving too rough of a beat-down when you’re working on them? More and harder is not always better, though sometimes it’s hard to glean that from the Mobility Wod (Kelly has always catered strongly to his original CrossFit audience, who respond well to promises of pain and intensity; he presents mobbing to them like a dare). Consistently applying appropriate doses over days, weeks, or months might yield the best results.
It should also be taken into account that, when your tissues are really messed up and stiff, they can get pretty sore the next day from being worked on. However, I would be conservative when applying mobility work to muscles recovering from soreness. A little mobility work is great for recovery, but if you’re super sore and beat up a hard mobility session might just make the microdamage linger.
As others have said, an issue as stubborn as this is unlikely to be JUST a mobility problem, and probably has some motor control issues associated with it. If you’re able to post some footage of yourself doing some squats / deadlifts, that would be very useful.
In the meantime, here is something I would suggest you try. Retaining the new range of motion you achieve from an acute dose of mobility work is contingent on you integrating that new range of motion in your movement, teaching your body to accept the new range on a neuromuscular level and absorb it into your motor pattern. Assuming your motor patterns are decent (before we see otherwise), try mobilizing your hamstrings and follow with Romanian deadlifts (with the empty bar for now), being very mindful of the downward phase of the movement and of when you reach the end of your range. Find hamstring tension at the bottom, acknowledge it for a moment, and then come back up. Repeat for a handful of reps, then return to mobilizing.
Given that you’ve been experiencing a lot of soreness and stiffness following hamstring-involved activities, be conservative at first, and gauge the appropriateness of this approach by how it affects you over a couple days. Did you improve your range of motion? Did you avoid getting super frickin’ sore?
Good luck, and keep us posted! The more information and footage you can provide, the more accurate we can be.