@Chris: Does the recipe from the Nero Wolfe cookbook say anything about dumping the milky/watery portion out of the pan before returning the butter to it to brown?
Clarified butter WILL NOT brown, that is the purpose for clarifying it. The milk solids are what brown. The portion that usually goes to the bottom will be the whey and the milk solids initially tend to form the "scum" on the top. To me it sounds like he's trying to suggest that you should pour the butter & solids off, dump out any whey, and then return the butter to the pan so you can heat it to the point of a dark brown without it splattering (which is caused by the water in the whey). 4 tablespoons of butter isn't going to have much whey in the first place so just cook the whole butter to the beurre noir point.
I think the problem is actually not the heating, but the refrigeration!
Consider: bacon fat solidifies easily and thickly, and does so even at room temperature. When you throw it in the fridge, the micro-droplets of bacon fat will turn to solids and clump together. These solid droplets are frozen in place when solid, but when you thaw it, they melt and reveal how wrecked your emulsion is. Now, you could add additional emulsifying agents (lecithin, extra yolks) but that's not really going to solve the problem of refrigeration.
The solution is to break up the bacon fat as it melts, and re-establish the emulsion before it can break. To do this, you have to whisk constantly as you gently heat the mayonnaise, generally in a warm water bath.
How to execute this in a restaurant setting:
Prep a big batch of bacon-mayo and throw it in the fridge. Just before service, warm some water in a pot and throw a cup of the mayo in a small bain marie or metal 6th hotel pan. Immerse the bain/pan in the pot, and whisk it as it melts. Hold the mayonnaise for service in water warm enough to melt bacon fat, and DISCARD THE WARM MAYONNAISE EVERY TWO HOURS AND THAW A FRESH BATCH. Make sure no cooks get lazy about that -- it's a food safety problem. Ideally, you should be using pasteurized eggs to reduce the risk of salmonella. Basically, you're treating your mayonnaise like a Hollandaise or Bearnaise.
I've found that the thawing trick works fairly well for home hollandaise (which most people say shouldn't refrigerate), and which does the same thing if heated fast. It should apply to easily-broken mayonnaise too.
Best Answer
I'm quite sure being able to reheat beurre blanc is a superpower without a superhero. Your efforts are commendable but I think inevitably futile, I'm sorry to say.
The problem is not that it splits while heating up. The problem is that the sauce splits while cooling down. This is caused by the butter solidifying. When heating it back up again, it will simply become visible that the sauce has split.
It's unfortunate, but you're probably best off not making too much beurre blanc. If you still have some left over, it's a great component to use in a cream-based sauce. Also, if you really want to make a beurre blanc that you can cool down, you could experiment with adding cream. But even though it might turn out to be a nice sauce, it's not the real thing.