United and Star Alliance airline partners Lufthansa, Swiss, Air Canada and Brussels Airlines have low summer fares for Moscow DME at $704 round trip for travel June through August, primarily for departures on Saturday, Sunday and Monday from Houston.
Google Flights shows most Sunday and Monday departure dates in July and August with $705 Star Alliance fares, and some Saturdays. OneWorld airlines are 2x the ticket price.
United Airlines Houston IAH – Moscow DME
$710.55 Sunday July 3 – Wednesday July 13
I found prices a low as $703.45 flying Air Canada and Brussels Airlines outbound with Swiss and United on return Aug 8-16.