Short answer: whatever you do, you will most likely be wrong.

Long answer:

The absolutely correct way to do it would be at-source during EPMA measurement. This is because the excess oxygen, which does not exist, is taken into consideration in ZAF correction procedures. Supplement that with measurement of light elements (H2O for micas, CO2 for other minerals, Li+Be on LAICPMS, Li being particularly important for micas).

Some EPMA software knows how to do it, Probe for EPMA is one of them. I know that JEOL does not do it. Not sure about Cameca, didn't use that one. Alternatively, you can do an offline ZAF correction using the freely available CalcZAF: https://probesoftware.com/Technical.html

Although the difference between that and just using a spreadsheet is very small, it can get to a noticeable systematic error when you have light elements (Mg, Al) together with high F (e.g., fluorphlogopite), or when you have things like chlorapatite with high Si.

Any method that does not involve appropriate ZAF correction will likely lead to non-ideal results, which may or may not be detrimental, depending on what you're doing with the data and what you need it for. In any case, as you noticed yourself, opinions on the correct way to do it vary between people, some are more correct than others. My own personal opinion is to do normalisation based on cations, not anions. The most abundant anion (oxygen) is not measured, so I reckon normalising to a "guess" is more error-prone than other methods. Also remember that your OH is not measured (and each H has 0.5 O associated with it), taking your totals down in a very non-precise way. Some minerals can also have an "oxy" endmember (including micas https://www.mindat.org/min-39713.html), which simply cannot be analysed, but can only be inferred once you're 100% certain everything else, ideally with additional confirmation by single crystal XRD, is correct.

I agree with Dr. Anenburg, and in most cases you can use sum of cations at a certain site. For example, ∑ (P+Si+...)=3 apfu is normally used for apatite supergroup minerals. For JEOL EPMA, oxide mass is actually calculated based on cation (adding oxygen for stoichiometry), so you would get excess oxygen for Cl-F-bearing minerals if you only simply add all oxides up. The final mass result for Cl-F-bearing minerals shown by JEOL has already considering excess oxygen based on F and Cl mass, by adding up all oxides, F and Cl mass, and then minus 0.23 Cl and 0.42 F. Why 0.23 Cl and 0.42 F? It use F and Cl to access excess oxygen by electrovalence balance.

I think you opened the Pandora box ;)

I will not comment on the involvement of oxygen in the EPMA matrix correction because I am not a specialist in this aspect. So I will only talk about the formulae computation itself.

First of all, for spreadsheet computation, the short answer is that it doesn't matter what is happening in your OH site (or O(4) site for biotite), as long as the substitution is not balanced by another site, i.e., you don't have species that have a charge different than -1, like O2-. So using 22 or 11 oxygens even with significant F or Cl doesn't change anything.

The reason for that is that the 11 or 22 equivalent oxygen are not computed using oxygen, but in fact from cations from all sites except the OH site. If you sum up the positive charges for phlogopite for example, you will end up with 22 or 44 positive charges, again without the H+ from the OH site. But, there is a long debate about whether there are vacancies, especially in the interlayer and octahedral sites, so normalizing to that would artificially increase your cations because that would mean that you assume there are no vacancies. So the original idea was to translate this into oxygens since they are the anions that are counterbalancing the positive charges.

As for using only cations from one site, first of all, the interlayer and octahedral site might have various degrees of vacancies, which exclude them. Then the tricky part is that most substitutions are involving more than one site, for example, if you look at the tetrahedral site, Al will be in this site but also in the octahedral site so you cannot normalize the Al2O3 and SiO2 moles to 4 or 8 and use that factor to compute the rest of the cations.

There have been alternative scheme proposed, such as the 14 + Ti normalizing scheme that assume that all Ti is incorporated through the Ti-vacancy substitution (which is very unlikely) or iterating through all negative charges to end up with 24 charges when you have measured H2O directly (Cesare et al. 2008).

In our 2018 Contribution to Mineralogy and Geochemistry paper, I did both the 22 oxygen and the 24 oxygen schemes since we measured H2O via SIMS and the difference was negligible since there was almost no O2- component. So unless you are working in a very low H2O activity setting where you probably have a non negligible oxy-component, I would stick to the 22 oxygen scheme computation and remember that my octahedral and interlayer vacancies are probably overestimated. Otherwise it becomes much more tricky and you should probably think about measuring at least H2O (and possibly Fe3+ but in-situ you have to access synchrotron facilities which is not that easy).