The best and only constitutional solution is to publicly fund all federal elections. 2 billion a year could fully fund all congressional elections. You don't even need to fund the presidential election because the two parties raise more than enough money themselves. They are already buying literally all the commercial time on TV in swing states. More money doesn't provide much marginal benefit at that stage.

That wouldn't prevent companies from funding PACs, but it would greatly reduce their influence.

I'm not overly familiar with Lessig, but I believe he proposed the public funding option on a RealTime with Bill Mayer.

I'd also increase individual donation limits. Upper Middle Class people throwing 20k to a campaign for shits and giggles doesn't carry the same sort of risk as Boeing giving 500k and then asking for a defense contract.