I believe triceps-tendon irritation stems from 1) not enough ‘off’ days, and 2) poor exercise sequencing.
To address #1, I would suggest clustering all your triceps-intensive work (ie, pressing movements and direct tri work) on a single training day. This will allow maximal recovery time for the tendons.
Working with Meadows opened my eyes to the importance of #2. Since I’ve started programming JM’s way, I haven’t had any trouble with my triceps insertions (and they used to hurt constantly). Think of your Triceps work as being divided into three phases. Each phase has a specific goal, and each prepares you for the following phase.
1) Activation/warm-up phase;
2) hypertrophy-work phase; and
3) stretch phase.
IMO, the key to a tendon-sparing triceps workout is a thorough and proper warm-up. The goal is to engorge the muscle with as much blood as possible, but without putting undue stress on the tendon. To accomplish this, the exercise should be one that allows a hard squeeze against resistance in the flexed position (I prefer rope pulldowns, but kickbacks work really well too). The weight should be very light, allowing reps in the 20-30 range. **This is key**: The ROM must be kept very short–from the ‘almost fully flexed’ to the ‘fully flexed’ position. (Basically, you just break the locked-out position to the tune of a few inches, then go right back into it.) Squeeze your tris like a maniac throughout. Do 3-4 sets, with only ~30 seconds rest between.
Your tris should feel absolutely blown up at this point. That is a good thing. NOW your tendons are ready for some heavy work. Heavy pushdowns, dips, CGBP (another reason to do tris on Chest day, BTW), etc–pretty much anything EXCEPT skullcrushers (more on this below). Reps in the hypertrophy range, 8-12 or so. Do as many sets as needed.
Only NOW are the tendons ready for some careful stretching. The last triceps exercise emphasizes the stretch position. Skullcrushers with the head hanging off the bench and the bar reaching back towards the floor are great here (I do them with DBs, which allows me to tweak the hand position as needed). As with the activation phase, the weights are lighter, and the reps higher–10-20/set is probably ideal. 2-3 sets are plenty IMO.
At the end, your tris will be fried, but your tendons will not.