First off, it sounds like someone else is in total control of your job!!
You need to take the bull by the horns and man up. Do you have any documentation to get the point across and how important this is. Do you have the NWFA Technical manual? That one bible, will set you free!
At this point what I would do, is to compose a very specific well worded waiver of liability. In it, state what they want done. the conditions they want it installed as, what the standards and guidelines state. State what is going to happen if it is installed like they wish. Then in BOLD TYPE, State, " This installation is
only meant to be a temporary installation, as the understanding has been met and agreed, with all parties involved with this contract, that this installation as specified by ___________is prone to fail, by not following documented industry standards. Any corrections or replacement after installation is complete, will be billed and charged per our most recent price list. Then get the person you have a contract with, to sign it. If you are subcontracting through a GC, get both the home owner and GC to sign it, or walk away from the project.
This jobsite is not even ready to start acclimation, much less a full installation.
Use the long probes on your moisture meter, or some finish nails to drive into the subfloor in depth increments. You want to see if the deeper you go into the subfloor, the moisture % does not keep rising.
From what I hear from your post, the floor is going to cup severely, it may even buckle. When that happens, your looking at some expensive firewood, that does not taste any better eating it, even with a little salt & pepper.