My choir (I am a BWTSTP*) goes overboard about pronouncing Latin; for French composers we use French Latin, for German ones German Latin . . . if it were up to me I would stick with Italian Latin, since they are at least on the spot, even if they have demonstrably altered their pronunciation over the centuries.

But it's all for the fun of it in the end. Nobody knows how it sounded 2000 years ago.
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*Baritone Willing To Sing Tenor Parts