I agree with Clemi - you should use a host to book. Either the one you have already at Cherokee or the one Zeus mailed you.
The offers you're seeing are the ones they extend to a lot of players, with varying amounts, who haven't stayed with them in Vegas before but who have TR play at other TR locations.

I stay with CET in Vegas now but with them I've only stayed at Caesars. I'm a hotel snob and it's more than met my needs, I know my way around the place now and how and how long it takes to get from there to wherever else I want to go, so I've stuck with it.

I would just suggest that if you do go with PH or any property where there's only a certain type of room or above that you'd find acceptable, and you get booked in that room, check back on that reservation as it gets closer to the trip to make sure they haven't demoted you to a lower room that may not be acceptable. This hasn't happened to me in Vegas, where I've always worked with the same host. But at other locations I've been able to book the "Acceptable to me" room online as comped - I'm a planner so I normally do my reservations months in advance - only to find as it gets closer to the time that they've downgraded my reservation to a lower level room. I'm a Seven Stars and this has happened to me at locations that I have planned to visit for the first time during somewhat higher occupancy periods (like AC in summer).