Replace term limits with a prohibition on consecutive terms and on fund raising or campaigning for a successor while in office.
Political experience should lead to statesmanship, but generally leads to more adept corruption instead. Professional politicians spend their time protecting their jobs and stealing for their corporate masters. Eliminate the breed entirely by making politics a means to serve the voters rather than a self-serving career.
Replace professional politicians with Mr. Smiths. Representatives should spend their full term doing their jobs instead of running for re-election or courting special interests. They should be drawn from the communities in which they are intimately involved.
Their election future reelection, if any, should be based on their accomplishments in their previous term, and the effects of their actions in the interim between terms.
Keeping things going would require that the old hands work as consultants for each batch of newbies. It would be the newbies' responsibility to decide how much of the old slime to wallow in and how much to rise above.