supplementary characters in FreeTDS
Things to look at / try:


Looking at the documentation again (now that you have posted the config file and configuration options), I think your setting of client charset is incorrect. You specify --with-iconv-char-enc=UTF-8 when configuring the build for the ODBC driver, so I suspect you need to also use UTF-8 when specifying the client charset option (or whatever encoding your app code is using).
Try rebuilding FreeTDS with --enable-odbc-wide-tests. This might help narrow down where the issue is (assuming the test uses Supplementary Characters).
Did you see the note about "Version 0.95 removed support for iconv" on the FreeTDS page for How to build: Configure and make? Not sure what, if any, impact this has, but if nothing else helps then you need to verify this part (i.e. that your build of iconv works and that it is being used).
Looking at the unixODBC website, the main page has a version history and you claim to be using 2.3.0 which, according to that history, was released in April 20th, 2010 (almost 6 years ago). Since then there have been several "wide character"-related bug fixes, as well as many other fixes. Even if some other change (#1 perhaps) fixes the immediate issue, I would still upgrade to the most recent version of this driver, 2.3.4, which was released on August 31st, 2015.
Something to consider, perhaps, but if the Microsoft driver does work, why not just switch to using that?