Encore has now opened up their 2 bedroom apartments and 3 bedroom duplex apartments for booking. They show up online but don't list as available. You have to call in to get the rates and/or book them. I was told these are the rates:

2 bedroom apartment (3,475 sq ft) - $1400 on every available date
3 bedroom duplex apartment (5,829 sq ft) - $3500 on weekdays/$5000 on weekends

They are both showing to be available on a weekend that I'm looking at traveling to Vegas (Sep 17-21). The agent told me that most weekdays are available but weekends have very limited availability as they are typically reserved by casino hosts for their guests.