Rather than paying Congressional Representatives higher salaries to maintain multiple home, in their home state and DC, provide military style barrack housing for their time in DC. Their function is to make legistative decisions in an efficient cost effective way - do the right thing at the right time.
Barrack style housing encourages an atmosphere of shared pain (think military housing and HUD housing) and reinforces the reason elected officials are in DC. It reduces the overall cost of congressional operations by reducing the time the Congress is in session. Consider housing their support staff in a similar manner. This opens the opportunity to reduce salaries as there is reduction is housing costs and transportation costs.