What basis of pronunciation would you use for Latin? Esperanto-based? Florentine? Milanese? A compromise? An interesting idea I once had, for any state that used Latin as an official language, would be to retain an Italianate pronunciation (based on OTL Standard Italian) for the consonants only, whilst going for Milanese-like pronunciation in the vowels - this means that in addition to the basic vowels of Standard Italian, there would also be two additional vowels /ø/ and /y/ (similar to but different from French) plus usage of vowel length and nasality as important phonemic distinctions.
Note, too, that the Latin in use in the Vatican is actually a hybrid of both the Classical Latin nominal system but a verbal system more in tune with Medieval Latin, IIRC, so even there the Latin is not totally like the Classical form, even if the latter is the ideal.