The Hyatt is the other top-end option, which is where we stayed a couple of years ago. The room was a little 'functional' but the location is fantastic and overall it is not a bad place. I've read some bad stuff about the R-C but to be honest haven't looked at the reviews for a while.
Your best bet - given Moscow prices - would be Hyatt points if you could do an exchange with someone who has some.
Flying - don't use BA because they have the clapped out 767's. BMI is the only way to do this, especially given the exceptionally low number of BMI miles required. Laughably it is far, far cheaper to join Diamond Club and buy the miles you need for a J redemption than actually buy a ticket.
Visa - it is not that difficult in London, not sure about Ireland. Book the hotel and they will fax you the form (with a warning they will charge your credit card if you later cancel the stay). You then simply drop it in at a visa service bureau (probably one in Dublin) who can take care of it in a few days. I use one very close to my office in London, although I believe that the Russians have now opened a 'proper' visa office in London which avoids the need to queue for 3 hours in the cold in Kensington.
If you're not arriving at the weekend, consider taking the train from DME as the traffic can be very, very, very bad indeed.