The FAA TCE must be working with/for an authorized ATO in order to legally give a 61.58 check as part of an approved course. As others have noted, it must also be done in an FAA approved simulator. Lowest prices for this can usually be found in Miami on NW 36th Street. Pan Am quotes just under $5000 for an approved B777 recurrent course and 61.58 check.
If you are doing this for ferry flights as SIC, it is not actually required under FAR 61.55 (g), you need only comply with 61.55 (b)(1), no need for (b)(2).