You may try the following:
Get in contact with the russian FBO handling your outbound flight.
They might be authorized to pick you up at your inbound and to transfer you upon arrival.
In that case they may organise a crew visa at the location. (2-4 hours waiting time)
Process is quicker if you provide them with passportdetails and copys in advance.
But be aware, this is a so called VIP Processing.
You know the prices in Russia? Quit a nightmare.
So if you do have some time, its better to follow the mentioned above.
Good Luck!