What would be the easiest method of removing FR-4 from a FCBGA chip
While I haven't done it myself, lots of people on the internet talk about depackaging various chips to see what is inside. They post photos I find fascinating.

Perhaps you could contact the people that run the following websites -- perhaps one or more of them knows how to take apart FCBGA chip packaging?


The Silicon Zoo: Unpackaging and Photographing Integrated Circuits
http://visual6502.org/ (In addition to the 6502, they've depackaged and posted detailed photos of the interiors of dozens of other chips)
http://www.lps.umd.edu/MicroelectronicsIntegration/MicroelectronicsCOTS.html
Sergei P. Skorobogatov describes using "hot fuming nitric acid" to depackage chips: a b
http://www.empf.org/empfasis/2009/June09/tech_tips_609.html mentions "mechanically by chiseling off the top with a fine razor and small hammer"