Understanding the nature of your PT due to my background as a subject matter expert for various military units around the world, allow me to offer the following generalized recommendations.If choosing only 2 exercises to complement your extant PT work, select swings and jerks. I’ll explain.
Swings give you all of full bodily conditioning you need while maintaining the closed, packed position on the shoulders (biomechanically, the most stable position for the shoulders.) I’d normally suggest the clean, but because the clean can include an element of scapular elevation, the shoulders can come unpacked and with the high volume of pullups, you may face over-training.
The swing will also be a good complement to the running volume, since it is the functional opposite to your gait; and with good range of motion, will help you maintain balance with improved hamstring strength (due to the eccentric loading phase on the back swing.)
In addition, most people find the greatest difficulty in learning shock absorption without significant training of a proper swing (by proper I mean a swing which is mechanically designed as a building block for the clean and snatch, like Fedorenko’s technique.) As a result, most people accumulate external rotator trauma from repeatedly drifting the bell externally (as if someone was beating you in arm wrestling.) This can be brutal to high volume pullup athletes like crossfitters and climbers.
The jerk is my second recommendation. Normally, I’d suggest the Yawing Press, but because of the pullup volume, the press can be problematic since in both strict pullups and military presses, many people do not maintain shoulder pack, leading to rotator cuff strain (since the force transfers not to the load bearing structure, but to the soft tissue not designed to accommodate it.)
Here’s a free video tutorial on the Yawing Press:
The jerk, furthermore, is the functional opposite of the kipping pullup, and will contribute to the muscular rebalancing of your normal PT. I realize that you perform (primarily) strict pullups, but you still need to maintain structural counter-balancing. The jerk is the least intensive on the shoulder grind of the big 3 (press, push press and jerk), so I suspect it will be very helpful.
On the swings, I’d focus on heavy (32kg) and one-handed open switches to preserve your hands. That way you can maintain a modicum of strength while deployed. However, for the jerks, I’d suggest light (12-16kg), one-handed and view them primarily as a counter-balancing your pullups in order to prevent a future injury. Standard timed-sets apply, but we could discuss how to create a scheme which would progress upon your PT times if you wanted a bench-mark.
Be Safe Out There!