Tibetan White Crane drills punches by pivoting the body sideways, using the torque of the full-body pivot to get power for the punch. But the body turns all the way until you face sideways to the enemy. That is how we drill the punch, but not necessarily how we would use it in a fight. It is an exaggerated movement designed to teach and develop full-body connection.
When I was training Tracy Kenpo, we would stand in a square horse facing forward and drill punches by keeping the shoulders square to the front, and punching straight ahead. It seemed to me that we were relying on muscle power of the arm and shoulder, and not really engaging the body.
Because I was doing both, I ended up not pivoting far enough when doing white crane, and pivoting too far to no longer be square facing the front when doing kenpo.
My white crane Sifu would tell me, āpivot more, you arenāt going far enoughā.
My kenpo teacher would tell me, āstop pivoting, keep your shoulders straight.ā
I was doing it wrong for each method, based on the parameters and standards of each method. Practicing kenpo was undermining my crane, and vice-versa.
Now, I could certainly continue to practice both methods. I could be very careful to compartmentalise my training and practice both methods, and try to not let them affect each other. But this is not efficient training.
If you want to be able to punch, you want to train a consistent method so that the skill becomes internalized within you and your body harnesses the power consistently and automatically.
What you do not need is multiple ways to throw a punch, multiple ways to harness power for the same technique. That inconsistency in the method will slow your development and confuse your automatic response if you need to throw a punch, under pressure. In terms of training, it is like trying to drive your car to the next town, but you canāt decide which of two routes to take. You get two miles down the road and then change your mind, so you go back and take the other route, but when you get two miles down the road you change your mind again and go back to the first route. And then again and again. You never reach the other town.
Pick a route and stick with it.
Pick a method and stick with it.
Training multiple systems that have conflicting methodology is like that. You simply need a reliable and effective punch. You DO NOT need two or five or eight different ways to power your punch. That may be of interest academically, but ultimately is not terribly useful.
So the incompatibility lies in the methodology, and not necessarily the body of techniques. You can swap and trade and adopt techniques from any other system, as long as they are compatible with a consistent methodology, or if the realm of combat is so different that there really is no overlap with the methodology.
I can understand your pain.
The first day that I started to train WC, I already had long fist training for 8 years. When I did the 1st WC form, instead of freezing body and only moved my arms. I rotated my body anyway.
IMO, I either do a bad WC, or I no longer believe in my long fist training. I just can't do anything in between.
Even today, I still believe in
move the body and not moving the arm > move the arm and not moving the body.
I think (as I mentioned in my earlier comment) that the key to integrating different methods is to understand why they are done differently and the trade-offs being implemented in a given method.
Regarding Kenpo, practitioners do not actually fight or spar standing in a horse stance square to an opponent and throwing punches straight ahead with no body rotation. That's a drill. In order to decide whether the drill is compatible with a different style, you'd need to understand what the purpose of the drill is. Personally, I suspect that the exercise may have been adopted from some earlier style and kept for tradition's sake without comprehension of its meaning, but I'm open to being corrected on that point.
Wing Chun, on the other hand, does advocate fighting with shoulders square to an opponent. Hip/body rotation can be added to a punch, but usually only when accompanied by an angle shift relative to the opponent, so the practitioner still ends up with shoulders squared off after the rotation. Since this is more of a special case, most lineages don't seem to include it in the first form.
The purpose of this squared stance is to allow both hands to be equally and simultaneously engaged in the fight. The downside is the significant penalty to power due to the lack of body/hip rotation. Despite this penalty, WC practitioners can develop functional (if not exceptional) power. The main engines for this power are "elbow power" (which actually originates in the back muscles and is transmitted through the arms via good structure not arm strength) and forward body motion, typically from a pull step.
My primary art for punching is western boxing, which relies heavily on body/hip rotation for power. It also uses forward body motion for power, but typically with a push step or drop step instead of a pull step.
What I've found is that I can integrate "elbow power" into most of my boxing punches with no problem. The power still starts with my feet, I still rotate my body, but now the structure for transmitting the power from my back through my elbow is cleaner. Even for punches where that exact structure doesn't apply (like an overhand right), I am now more aware of structure principles in general.
For the body movement, I can use push steps, pull steps, drop steps, or some combination, depending on where my feet need to be at a given moment.
Bottom line, I'm not any sort of WC expert, but WC training has given me some subtle tools to make my boxing better. To be clear, there are plenty of boxers out there who use these same kinds of subtle body dynamics. The difference is, they aren't generally taught explicitly in boxing. Boxers are given the big tools for power generation, then spend countless hours throwing punches. Along the way, many of them subconsciously pick up these nuances for extra power. In contrast, WC opts not to use the big power generation tools and so it can develop more conscious awareness of some of the smaller tools.