Apostrophes were once used in a lot of plural cases (I've said more on this herehere) and while some such cases are now completely obsolete, some are still used to varying degrees.
The case of pluralising a single letter is perhaps the strongest survivor of the pluralising apostrophe (and indeed even in the case of pluralising letter grades, as despite your claim one can indeed find "She got five A’s and two B’s" and similar uses today*). It avoids a tendency to consider the forms ts as a word and even more so is, since there of course is already a word is. (Also the English words as and us and abbreviations like vs).
So, considering that apostrophes for plurals perhaps shouldn't stick in your craw quite as much as it does, (i.e. fine as a personal preference, but not "incorrect"), and considering the various points you've made, there's no perfect answer as to "which is it?" and all three are found in different styles of correct contemporary use.
I'd add the possibility of italicising the letter:
I just need to go through it once more to dot the is and cross the ts.
Which is my personal preference when markup is possible, but not the sole "correct" choice, either.
*Though there are style-guides that are half-way between the two, in that they require plurals of capitals to have no apostrophe but plurals of lower-case letters to have an apostrophe, and so would have "Taking care to dot the i's and cross the t's meant she got As in all her exams".