Lubbock is nowhere close to Dallas, have no fear of Tuberville. I lived in Texas for most of my life and can assure you that the distance between Lubbock and Dallas is more than a minor inconvenience (5 hours by car).
Being an airplane mechanic the only way I could think of finding out what the tail numbers are of Mr. Haslam's plane were to go to the FAA registry and this is what I came up with
1. I searched under the company which is Pilot Corporation. This gave me the tail number to a nice size business jet. The tail number or N-number is 353H. This tail number is blocked on FlightAware so no luck there.
2. If you search under the name Haslam it brings up a plane under the name charles haslam but it is just a cessna 177 (small private aircraft not business jet).
Looks like we are out of luck on the aircraft tracking side of things...
I know for a fact that Haslam's jet picked up Dooley when he was hired.
"If everybody is thinking alike, then somebody isn't thinking." Gen. George S. Patton