How should I pick a flour volume to weight conversion for an arbitrary recipe?

This may seem to be an overly simplistic response, but if it's in a decent cookbook that deals with baking, the book often has an introduction or appendix or chapter that describes how to measure flour. If it does, I measure the flour according to their directions, which can give a weight estimate. Older cookbooks tend to advocate a lot of sifting before weighing (in my experience). Newer ones sometimes mention spooning then leveling. And I've seen at least a couple which just admit they scoop and sweep.

If the recipe is from a book without such instructions or an internet resource without such instructions, I generally avoid it unless it's a type of recipe where I know exact flour measurement is unlikely to have a big impact. If I end up using such a recipe with no guidance on flour measurement, I sometimes try to take the era of the source into account if I know. Otherwise, I'm not sure my personal practice matters, because I'm just guessing -- like anyone else who answers this question will likely be. (Frankly, I worry this question is likely to turn into a poll.)

What to do

I think you have to forget the idea of a guess being somehow "better" in the sense of giving you the "least error" and treat all the values within some interval (which seems to be the 4 to 5 ounce interval) as equally likely to give you "the least error"*. So simply choose a value from the interval based on some other criteria (convenience for you, aversion to different types of error, suspicion that your own measurement errors might not be symmetrically distributed, throwing a dice, whatever) and stick with it as the best guess.

My personal preference is 4.23 ounces, but I don't claim that this is the best choice for everyone, and certainly not that it more frequently hits what the recipe author uses.

A sampling of what established authors use

This is what Shirley O'Corriher has to say on the topic:

I used to measure as I was trained: by placing the measuring cup on the counter, spooning flour into it, and levelling it off with a straightedge. Through years of teaching, I observed that my students measured by dipping the measuring cup into the flour and leveling it by pressing it against the inside of the bag. This is actually 1 to 2 tablespoons more flour per cup than I was getting. [... T]his is the way most home cooks measure [...]. If you prefer to work by weight, a cup of bread flour when I measure this way weighs 5.6 ounces.

Peter Reinhart gives both weight and volume for each recipe in Bread baker's apprentice and uses 4.5 ounces per cup.

Rose Levi Beranbaum gives both weight and volume for each recipe in The cake bible, and uses 3.5 ounces per cup of "sifted cake flour".

America's test kitchen has a conversion table in The new best recipe: 1 cup AP flour is 5 ounces.

Jeff Potter, in Cooking for geeks (not as influential as the other authors, but somebody who is obsessive about basing everything on solid data) uses 4.5 ounces per cup.

Simple statistics on that sample

We have an interval between 3.5 and 5.6 ounces, with a mean of (rounded) 4 ounces and median of 4.5 ounces. This is quite close to your own sampling of sources.

My recommendations

First, if you really want to go towards good guesses, you may want to start treating recipes from different sources differently. It seems that home cooks tend to use more flour per cup than professionals - the two high numbers in the range are from a book made with the explicit purpose to have as many home cooks as possible achieve consistently good results, and from an author who adjusted her measurements to suit home cooks' habits. So, you may want to settle on one number for recipes created by classically trained cooks and another one for recipes from those coming from a history of home cooking (even if they have turned into professional recipe authors).

Second, even though statistically, your best bet is to assume a normal distribution*, I would advise to not use the middle of the sampled range, but a lower number. Why? Tender baked goods such as cakes, crepes, etc. tend to taste richer with less flour, so erring on the side of little flour is going to give you a result which most eaters prefer, unless it is so reduced that it gives you structural problems (in which case, you simply have to redo the recipe with more flour - if you are too averse to such surprises, it is probably best to stop using volumetric recipes at all). Breads on the other hand are highly dependent on a number of parameters of the exact flour used which are never accessible for the home cook, so the ratio given in a recipe is just a starting point, you are meant to adjust it a bit if the dough texture is wrong. And adjusting towards more flour is always easier than adjusting towards more liquid.

So these numbers suggest that you should go for something between 4 to 4.5 ounces per cup. I personally like using 120 g because it is easy to do gram-based math in my head with that number, and it makes for easy round ratios with liquids converted to 240 grams per cup. These 120 g happen to be 4.23 ounces. I don't think I have had too many recipes fail from bad flour amounts.

* Technically, what I am saying is that apparently our measurement error (of authors' intents and home cooks' measuring results, not of ounces of flour per cup) is so large that there is not enough information in the world to give you a sensible point estimate, and what you have to work with is an informal confidence interval. Which goes against many of our expectations, but is actually quite a common occurrence. And it is not somehow less scientific than working with "the right number".

* There probably are several such distributions, one for e.g. home cooks scooping bread flour and leveling it against the bag, another for pastry professionals scooping sifted flour and leveling it with a straightedge, etc., and then the sum of those should be normally distributed. And I see no reasons to assume a skewed distribution for any of the one-context distributions.