It's very easy: a lot of larger hotels can do it for you, but it's easier to go through an independent visa support agency - especially as you're staying at two different hotels. just google 'Russian visa support' and you'll see lots of choices. I'd recommend the one I've used - google 'liga consultant Russia' and you'll find it - Liga Consultant: you fill out a form giving full details of you, your passport, your trip itinerary and hotels/towns you're staying in. They will more or less immediately email back to you the confirmation and voucher. You just print off a copy of each, that will do fine to go with your visa application. You don't need original copies of these. This will cost 800 roubles per person ( about €11 euro)/ You'll have to send over a faxed or email attachment copy of the credit card you're paying with (back &front) and similarly a good copy of your passport main identity page. I've used them 3 times recently, they're reliable, efficient, helpful - and trustworthy.

We were never there that late at night but it seemed like the kind of place that had enough going on that they would have that covered. Why not contact them directly and ask if they have 24 hour desk coverage?