As far as I know BA is fighting for a long time to get an early slot out of Moscow and it is believed that BA have moved from SVO to DME because they have been promised to get the morning slot to LHR out of DME, but it never happend due to strong lobby of SU.
There are no technical problems, both SVO and DME can easily accommodate an extra departure/arrival in the morning, it is pure political/economical grounds. Send now a slot request to slot coordinator for a charter or business jet arrival any time tomorrow morning to SVO and DME and you will get it straight away.
I don't think there are any issues on aircraft/crew safety during overnight stay, Moscow is not Kinshasa or Baghdad...