Another option for study in Moscow is Independent Study. Independent Study is an affordable alternative plus it is possible to find private tutors who are more flexible in terms of course content.
Generally finding a tutor is just word of mouth.
1. One option is to go to a Moscow university and post an ad for a private tutor on a bulletin board. While you're there take a stroll around at the foreign languages department and inquire with students and staff.
2. Another alternative is to contact a Moscow guide. Most of the guides have studied in foreign language departments and may be able to recommend friends or acquaintances who can help.