Liquid Layout has no purpose for a printed book and might be the source of your problem, as could be using the Page tool, but it's also possible you've run up against a bug I've seen reported a few times. I believe grouping the objects is a workaround for that bug, but it looks like you've already done that, or perahps this master is based on another so I'm not sure what the solution is here. What OS are you using? Is CS6 fully patched to 8.0.2?
One thing I would change (though probably not related to the shifting) is how you've built the headers/footers. Each could be made from only a gray text frame and a black text frame, with appropriate text insets applied on the gray frame, and you should look into variables for changing the header and footer text.
what can you do?
Create a new set of master pages, copy/paste-in-place the elements of the master pages you have now and apply that set of master pages to the pages. See, if that works…
Btw. I don't think using the Pages tool in the life time of this document is causing this.
It's probably changing the size of the pages by using the features in Document Setup after creating the document.
But I could be wrong. Both features have their bugs. The Pages Tool when creating Alternate Layouts and exporting and then opening from IDML, the Document Setup feature when items from the master pages are applied after changing the size of the pages and pages are added ( I have to look up some details ).
Thank you so much for the suggestions. I think I'm going to try the option of opening a "virgin" file and copy and pasting the elements one by one. But I'm going to wait until they decide on the template design so I can do all at once. I'll be sure to respond and let you know how it goes. But I did want to thank you and Uwe for the suggestions.