For what it's worth, Max, according to Vox Latina in classical Latin the sounds of an unaccented i and an unaccented u were practically indistinguishable.
But!
What Jackie says is right: "Singing pronunciation does or should differ. The vowels in Italianate Church Latin are pure Italian vowels ah, eh, ee, oh and oo none of which are diphthongs.
But, wait! That's not all!
There is also German Church Latin. Most of the noticeable differences in German Church Latin have to do with consonant pronunciation but the long e seems to be undergoing a Great Vowel Movement® similar to the Great Vowel Shift that English underwent in the 16th and 17th centuries and is pronounced rather more towards the sound of the long i.
Carmina Burana is however largely *not Church Latin (despite having been collected and even in some cases written by monks) and therefore not subject, strictly speaking, to the rules of Church Latin pronunciation. If you are singing in a group situation you will be subject to the dictates of the director. If you are singing by yourself, feel free to pronounce any way you want. I, for example, in the privacy of my own shower or automobile (or even when serenading my favorite phone callee) when I indulge in a stirring rendition of The Swan Song from Carmina Burana will, if doing my own setting, pronounce cygnus as tsinknoos.
