On page 44 of the fourth edition of Greene and Wuts there is a method for removing methyl esters from amino acids protected with CBZ, BOC, or FMOC. Yields of the 5-oxazolidinone intermediates were 25-90% (some BOC-protected amino acid esters gave low yields). These were hydrolyzed using sodium bicarbonate in water/methanol at reflux for 5-10 minutes. I believe that this two-step procedure removed the FMOC group in the second step, something that Greene's book did not indicate. This sounds like a good method to hydrolyze a methyl ester in the presence of the CBZ protecting group, but it is not suitable for your application.
Allevi P, Anastasia M 2003 Tet. Lett. 44:7663-7665 doi:10.1016/j.tetlet.2003.08.028