And, to be honest, I don't even know what the difference between the other two is.
According to this
, じっぷん is the most "correct" one (maybe it would be more appropriate to say "regular"), and じゅっぷん was formed by analogy with other compounds where the reading of the first kanji is じゅつ (and where gemination occurs). Now, as you probably know, じゅっぷん is more common.
I think calling it an ordinal number in the case of martial arts is more of a convention than anything. I know the usual way to say it in English is "fourth dan", but I don't think "four dan" would be wrong. Compare "5th grade" versus "grade 5" in English -- the latter isn't particularly common, but it exists, and uses a cardinal number despite meaning exactly the same thing.
I understand your point, but since "5" in "grade 5" doesn't represent a quantity and seems to have the function of an ordinal number, I think we should consider it an ordinal number. It wouldn't function as an ordinal if, say, "1st grade" were "grade 3", "2nd grade" were "grade 5" and "3rd grade", "grade 1" (i.e in this case it would only be the names of the different grades), but it happens not to be the case.
In fact, it makes me think of what was said in the thread about adjectives used as adverbs ; "sure" instead of "surely" and "grade 5" instead of "fifth grade" look rather similar... just my opinion !
And now, a little counter-argument : one could say that "5" in "grade 5" is only a name too, based on the actual order of the grades (and as such, matches the ordinal numbers that would otherwise be used). That would seem reasonable too.
But in any case, 四 in the two 四段's are different, I think -- which doesn't necessarily mean they should behave differently, of course ; the point is that it would be more likely. Anyways, as spin13 and NocturnalOcean have said, both よん and よ appear to be acceptable.