Here are the top sectors:
http://www.opensecrets.org/lobby/top.php?indexType=c
Misc Business $5,170,910,867
Health $5,133,518,315
Finance/Insur/RealEst $5,103,694,206
Communic/Electronics $4,242,220,479
Energy/Nat Resource $3,805,405,061
Other $2,778,387,216
Transportation $2,658,736,620
Ideology/Single-Issue $1,726,532,260
Agribusiness $1,506,658,475
Defense $1,471,380,620
Construction $565,657,978
Labor $518,071,553
Lawyers & Lobbyists $395,005,851
#2 is health care. They lobby for spending. You have to get govt out of health care. Merely slowing Medicare growth by 700 billion over 10 years is a major campaign issue that cold determine the outcome of the presidential election. Getting govt entirely out of health care is not going to happen. That means your "best solution" is completely unrealistic.
#3 is finance. They lobby for deregulation. So if you get rid of all the regulations, then they won't have a reason to lobby. Giving them everything they want so they won't have to spend money corrupting politicians is called "giving in". It's about as sensible as trying to shut down the mafia by repealing all the laws they break.
#5 is energy. Get rid of all the laws that protect the environment and no reason to lobby. Once again, your solution is tossing the baby out with the bath water.
#9 is defense. They lobby for spending. Defense spending is not going away. Best you can do is cut defense spending and they will lobby as much against defense cuts as they lobby for increased spending. Again, your "best solution" is simply not realistic.
There is always a simple "libertarian" solution to a complex problem and it's always wrong.