Pete,
First, my condolences to you and your first responder brothers for the tragedy in Boston today. I am sure the fire fighting brotherhood mourns deeply tonight
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Notwithstanding that technology has changed since I stepped away from the brush, I never heard oil over latex was danger, to the contrary, it was the poor latexes of the 70's that could not be applied successfully over oils.
Now if there is latex over calcimine, it will be coming off in sheets with a chalky residue on the backside - sometimes more than just a residue.
Even if you removed all flaking paint, it would be tenuous to apply another coat of anything over what latex remains.
Latex painted over calcimine that is peeling is a total crap shoot if you can't remove it all and wash the calcimine off.
This is why I said RUN.
IMO, if you can't do a thorough job, it isn't worth doing anything.
again, this is why I overlay without even attempting any remediation.
Let's hope you do not find calcimine as the root cause.