Several steps are needed to create the atmosphere you would consider optimal.
First, you need to be backed by the AD. Tell him/her what you are feeling and that you would rather have a team of 5-6 people who show up and try rather than a whole tea of slackers. If you get backing, then you are good-to-go.
Second, address the entire team with confidence. My suggestion is to possibly make a short speech about the team's lack of caring and poor attitude, and let them know that next year that it will not be tolerated. You will be very safe by this route. No one can claim innocence.
Third, Recruit. Look around on the soccer, lacrosse and basketball teams, and talk to a potential great long jumper, high jumper etc. Explain what their chances are in basketball vs. track. Also, guarentee that you will go above and beyond showing tapes of them to colleges. this combination of a coach who is really excited, flatters them, and gives them hope of playing in college will generate a real buzz. Be prepared for soms coaches backlash from other sports.
Fourth, and this is crucial, make a pre-season meeting with team and their parents. Tell them everything up front. This will prevent little Suzy from going home, crying about you and slanting the whole situation etc. The parents will know what is expected of their kid.
Fifth, do something to show you care. I found a xc invitational in Disney. I told the xc team about it in May, and we had carwashes, fundraisers etc. We had enough to take 12 kids. It was a great trip and made many other xc potentials jealous, and they came out the next year hoping to be part of that.
Doing these things will allow you to make demands and not hesitate. You will have the administration and parents backing.
You might even encourage parents to help like with bake sales. this will creat a family experience, and gets these parents preaching about you and supporting you.
Good luck