I voted for "egg-shell-sees (cease)" because that is the way my choral directors here want it pronounced. My personal favorite is "eks-chel-cease" for sung Latin. And according to my Latin I teacher (in 1951), Mrs. Bennett, it would have been "eks-kel-cease" in spoken Latin. (But we also said "Keye-sahr" for "Caesar" and "Waynee, Weedee, Weekee" for what "Keye-sahr" said. We also pronounced all the initial "H" letters, based on the idea that Latin was perfectly phonetic and there were no silent letters. Logic also indicates that "H"s would be pronounced whereever they occurred (not as part of a digraph) because it's a lot easier to say an "h" than it is to utter a glottal stop between adjacent vowels, and people are basically lazy.
We here in Texas are saddled with the (fairly) recent interpretations by Lloyd Pfautsch, with whom I disagree constantly. His pronouncements are contrary to all that I had been taught in the 40 years before I came to Texas. What makes him an expert? Did he find some old Romans living somewhere to ask? I've listened to many recordings of choirs in Europe singing Latin and they have been singing it their way for hundreds of years--why are they suddenly wrong?
(Rant off)
David