Your experience with the crust coloration issue reminds me of an extensive series of experiments that one of our members (who hasn't been around on this forum for quite a while) conducted and discussed at the PMQ Think Tank a few years ago. Like you, he used a natural leavening system although in his case he used a rather unorthodox and elaborate preferment system that included using a natural poolish and a natural sponge in series before incorporating the combination of preferments into the final dough. Like you, after much experimentation he got good crust flavors and textures but came up short in the crust coloration department. He was using some 00 flour as part of his flour blend (about one-quarter of it with the rest being a high-gluten flour), and he baked primarily in a steel pan, so there were those differences. He was already using a lot of honey, without much success in generating the desired crust color. He eventually tried using more honey, along with sugar, dried dairy whey and diastatic malt, in separate experiments, all with little improvement in the crust coloration. What I took away from his experiments is that if the "window" between the time the preferment (the first one in the member's case) is made and the time that the final dough is used to make a pizza is too long, as it appeared to have been in the member's case, the greater the risk or likelihood of ending up with too little residual sugar to contribute to final crust coloration.
Based on what I believe I learned from the above experience, my first instinct was to think about a way of shortening the "window" in your case. That is why I asked you if the latest milk kefir Lehmann poolish pizza was the best of the ones you have made. If you had said that it wasn't the best iteration of the milk kefir poolish Lehmann dough, I might have suggested using less milk kefir poolish or even switching from a kefir poolish to a kefir sponge with a lower activity level. The more kefir poolish that is used, as you did with your last experiment, the more of the formula flour is subjected to the prefermentation process. As a result, and given that a sponge preferment is more active and works faster because of its high hydration (100%), there is likely to be reduced levels of residual sugar in the dough at the time of baking. Also, a factor in your case is that, for some reason, the lactose in the final dough is either diminished or rendered ineffective in contributing to final crust coloration. Whether it is the "friendly bacteria" that is responsible we really don't know.
But, given that you were happiest with the last iteration of the milk kefir poolish Lehmann dough, and the "window" you used, I would like to see if we can come up with a solution within that framework.
One possibility that occurs to me is to use a lower bake temperature and a longer bake time, while being ready to use a pizza screen if necessary to lift the pizza off of the deck floor to keep the bottom of the crust from browning too much or even burning. I think your honey level should be able to tolerate that approach and if that approach works I think you should get better top crust coloration although that might be accompanied by a somewhat dryer crust. If that approach doesn't work, then you might try using more honey, again along with a pizza screen if necessary. Next, as another approach, would be to use more diastatic malt. I can't say that I am overly optimistic about this method, although it might contribute some additional crust color.
As you know, I am not an advocate of changing more than one variable at a time in my experiments since I can't tell what affects what, which means that I don't really learn from the experience. So that suggests conducting more than one experiment to sort things out. But that is your call. Ultimately, we may find that we have to find a way of shortening the "window" in some way, if not in time in some other way that is equivalent, such as using a different preferment to slow down the overall fermentation performance.