Additionally, the U.S. Constitution does not really permit blanket restrictions on employment for individuals. Among other things, this ties in with the 13th Amendment that bans slavery and indentured servitude. You also have a free speech right to lobby.
In fact, the current restrictions are probably unconstitutional.
Anyway, these measures are treating a symptom. The real problem is that the federal government is vastly too large in size and scope. Reduce the power and programs run by the federal government, and radically simplify the tax code, and you'll dry up the opportunities for corruption.