Back in 1997 my father-in-law gave me his mint black Zeiss Ikon Contaflex Super BC and 50/2.8 Pro Tessar lens. He purchased it 30 years earlier and put through only about ten rolls of film during the first 5 years he owned it and then put it in a drawer. So, because it sat for more than 20 years I sent it to Wolf Umbach who owned Z-V Service in Oriental, North Carolina. He CLA'd it and my Super BC still works beautifully today. I just called Wolf just a few minutes ago and, unfortunately, he no longer works on cameras. He also didn't know of anyone else still working on ZI Contaflex cameras these days (reliably).
I've heard good things about Essex but I didn't know they tackle Contaflex cameras. The price, $130, is right but I would ask them what their CLA involves and how they go about it. As mentioned above, these are complicated cameras to work on.
Good luck!
Marc