Dear Sir. Concerning your issue about the esterification of  a N-Boc protected amino acid. series of amino acid methyl ester hydrochlorides were prepared in good to excellent yields by the room temperature reaction of amino acids with methanol in the presence of trimethylchlorosilane. This method is not only compatible with natural amino acids, but also with other aromatic and aliphatic amino acids. I think the following below links may help you in your analysis:

http://naosite.lb.nagasaki-u.ac.jp/dspace/bitstream/10069/16631/1/kyoyoS33_01_01_t.pdf

http://www.organic-chemistry.org/protectivegroups/amino/boc-amino.htm

http://www.organic-chemistry.org/protectivegroups/amino/boc-amino.htm

Thanks