So my presses last night went pretty much the same. I had an old raggedy sleeve I used on that elbow to see if it would make a difference. When the snapping started to occur during the first working set, I put it on for the second and while it didn't stop the snapping, it made it much, much more comfortable and less distracting, like it was barely there. I then for my third set tried a wrap (I have for my knees in case that's ever an issue). I wrapped it tightly and it made no difference over the sleeve.
So I guess my final question to you is, if this doesn't actually go completely away this time, and it stays at such a mild level, am I going to be damaging the tendon by doing this over a long period of time?
I would think the human body would be somewhat able to cope with something mildly out of place like this, or at least adapt to it in a productive way. It doesn't hurt and right now isn't even uncomfortable with the sleeves.
Maybe. Maybe not. The most likely thing is that tendons have some ability to adapt to tendinopathy, although it appears to be vastly different than what we thought would happen. If you were somehow to quantify the number of diseased tendons in a well-broken in body of almost 50 years old, you might be horrified with the findings. Damage associated with activity is largely treatable and / or limiting, however, reduced muscle mass, loss of strength, sarcopenia, metabolic disease as a result of shying away from training is not as treatable and is self-limiting to the level that death is the great equalizer.