Improving mobility for reaching overhead (lat mobility)

I want to be able to press 2 kettlebells overhead at the same time. In order to do this without risk of shoulder injury, I need to be able to lock out both arms overhead.

I am currently exploring the Geoff Neupert P3 protocol, which aims to cure movement dysfunction by restoring motor control. From what I've observed so far on the Strongfirst P3 discussion thread, the "side lying" position seems to be the hardest to progress through for the majority of participants. I can do about 20 breaths, and 30 reps of each of the head movements, on each side. It took me a while to work up to these numbers. The next step in the progression is quite a jump in difficulty for me, so it's best for me to be patient and let my CNS and body develop at its own pace.

P3 practice so far has indeed seemed to loosen some muscles, including the lats. However, P3 is somewhat promoted as a mobility method for people who hate stretching, whereas sometimes I do get a nice satisfying feeling out of a good stretch once in a while. Tightness in the lats is one of the reasons I"ve had trouble reaching overhead. I found these suggested lat stretches.

In the past, I've explored flexibility/mobility exercises taught by GMB Fitness. Locomotion exercises are key components of the GMB way of achieving fitness goals, including flexibility/mobility. GMB trainer Adele Jackson posted four recommended locomotion exercises for improving mobility for reaching overhead, and general shoulder mobility, along with the recommendation to practice each movement for 1-4 minutes. These same exercises are mentioned in GMB's article How to Fix the 4 Most Common Shoulder Restrictions. The article recommends practicing the locomotion exercises after stretching. This helps consolidate the mobility gains from more isolated stretching exercises.