I notice that you do a lot of workouts that involve "learning to breathe under a load." I know this is an important component to many, if not all, of the athletes you train. My question is, how do you improve your athletes in this realm and how do you measure their improvement? I know you stress diaphragm breathing, but what adaptation is produced physiologically? Is one able to become more efficient with the limited supply of O2? Does the athlete learn to "get more" out of each breath?
Breathing efficiency is a fringe area, where charlatans and fakery abounds, but also the domain of the truly dedicated and to them come great rewards given appropriate energy and attention. There are techniques and devices to train them, ideas and methods, where science and anecdotal "evidence" both conflict and concur. I've spent a lot of time using a particular device and method to improve breathing efficiency, and to learn how to match frequency and tidal volume to different levels of effort, in different positions on the bike, undertaken at different speeds, etc. It's a deep rabbit hole, not easily explained. However ...
You can go down the "breathing training" rabbit hole quite a distance. There is a point of diminishing returns for strength/power or power-endurance athletes though (muscle power contributes more to the outcome than cardiovascular power does), while endurance athletes may benefit greatly. The ability to breathe against resistance is obvious for jiu-jitsu guys, wrestlers, etc., i.e. one can still get adequate O2 while being crushed by a guy on top if intercostals, diaphragm, etc. are strong enough to work against resistance, and to do so in a relaxed manner. This is also true for anyone carrying a load: firefighters, soldiers, police, climbers and ski mountaineers, etc.
What is less obvious to all athletes is "how to breathe" to maximize O2 uptake with minimum energy expenditure: the more efficiently one breathes the less O2 is used by the breathing musculature so the more is available to the skeletal (working) muscles. There are postural issues at play as well but I won't get into it now. To maximize O2 uptake for minimum energy expenditure can be as complicated as learning and practicing the ideal frequency/tidal volume of breathing for an individual athlete in a particular sport or as simple as understanding that the greater the quantity of CO2 exhaled the higher the volume of O2 may be taken in with each inhalation. Learning to exhale is the first step because for the most part we are only recycling the CO2 in the throat and top portion of the lungs. Using the breathing ladders can teach proper breathing form of course, but I believe the breathing ladders teach one how best to rest and recover, how to quickly reduce O2 demand, quickly drive HR down, etc. Each player seems to have a different trick for this, so there are many right answers to the problem - the ladders are a simple way to force the player to consider breathing and posture and how these relate to the quality of a rest period. When you say "periodization of breathing ladders" I take it to mean frequent "visits" to them, and while this is effective initially, for the player with no prior experience we learn the tricks quickly and must move on to other means thereafter.
Your "Jonescrawl" time improvement can derive from a bunch of things. O2 efficiency may be one of them but I think in the early stages of exposure other characteristics contribute more. I'd say that once all of the movement efficiencies and power-to-weight ratio are maxed-out then O2 efficiency becomes the last piece of the puzzle.