I stayed at the hotel in Moscow for the rest of the morning and got good sleep. My friend Ben had suggested that I take the overnight train, Red Arrow.
However, what I mostly needed was sleep and was worried I would not sleep on the train and would get in too early to check into the hotel. So, I just booked business class on the train that left around 10am and took my time to pack up and relax.
The train station was just steps from the hotel, but lugging my giant suitcase around in that heat is never fun. I found the business class lounge and was able to get a bit of breakfast and tea before finding my train and seat. I was originally sat on the aisle at a 4-person table, but an older Russian guy asked (in gestures) if I preferred the window, which I most definitely did. It is about a four-hour journey and we got a full 3 course meal, including appetizer, main, and dessert as long with a drink, which I got a Sapernavi wine.