Various folks I know continue to wrestle with the issue of courier services. So...I contacted a mail service called https://www.cdek.ru/ru/ who claims to ship docs from US/UK to Moscow with the shipper as a legal entity. Docs from Moscow to US/UK can be sent by a person or legal entity. Delivery can be door to door in the range of a week or so.

Rates range from 3000 to 7000 Rubles for a one page a4 doc, more or less.

I haven't used them and this is not an endorsement, but someone might need this service and could give it a try in a pinch. Recheck the rates, mine are approximate.