I keep getting stuck trying to hear "Mustang Sally" at 40 BPM in my head...

If you REALLY want to know the answer to the question of how to hire the top tier session players then find out who represents them.
Call the agent of one of them and explain what you need.
The artists have websites.
You need to hire one as the LEADER and he can acts as your liaison for the rest of the players.
He can suggest who is good and available.
He will need to be compensated for this, too.

Now, to be honest, you don't always need to hire the biggest names.
There are other great players in other cities and in the same cities as the top tier guys.
They might even be more inclined to work with you because they are not as booked.

It is important that you weigh where you sit and and where your production sits in the scheme of the world.
It would be far better to have some less known guys saying, "Yeah, this guy has some stuff he needs recorded and it isn't too bad, either. Wanna; do the date?" than to have a top tier guy saying, "I don't know who the hell this guy is, but I can squash this in between a few dates. We can make some money."
Neither will do a bad job because they are pros, but you'll get a bit more from the lesser known guys if you afre an unkown entity.

Remember, there is a whole industry in certain cities where studios record unknown artists and arange the whole thing. The artist is too intimidated by the whole situation (studio.. players) to question anything.
They knock out a standard arrangement and the "artist" gets a tape.
Bye, bye... call us if you get a deal.
They are not trying to screw anyone, but they do want to get your "dream money."
It is somewhat like running the ferris wheel at an amusement park.