Just to confuse matters: Medieval Latin scholars generally pronounced Latin according to the rules of their native language. That was because they had no way of knowing how Classical Latin was generally pronounced. Modern Ecclesiatical Latin is pronounced like Italian because the Vatican is in Italy and Western European Latin scholars evnetually accepted its Italian pronunciation as standard.

The reconstructed pronunciation of Classical Latin taught outside the Church is based on language history that was unknown in the Middle Ages.

The point is that an English-speaking cleric in the Middle Ages would likely pronounce Latin as if it were Middle English, which was pretty far from the Italian pronunciation. In such cases, "Ihesus" would indeed be "Jaysoos." (The history of how the letters "I" and "J" were pronounced and why is another story entirely.)

My two cents is that few medieval music fans are ready to hear, without warning, a Latin hymn sung as Middle English.

It would be interesting though.