Whether you believe we're living in a republic or a democracy, we're very possibly dancing around the crux of the issue by discussing campaign reform and the influence of lobbyists. Here's a suggestion:
"Resolved that all Congressional Districts be drawn with straight lines only and a maximum of 4 geographic corners."
This is not to say we don't need public financing of elections or that we shouldn't try to corral the influence of lobbyists.
At the very least, this idea would need to include exceptions for districts which are on coastlines or state boundary lines which are not "straight" lines.
Furthermore, while gerrymandering is a problem, this particular suggestion would likely result in several districts having drastically different populations. Part of why districts are sometimes drawn in amorphous shapes is due to the need to make them all roughly equivalent in population.
A better suggestion would be to determine that instead of districts being drawn by state legislatures, that each state legislature must instead appoint a Redistricting Committee, and that each such committee would consist of fifteen members not currently serving in any other elected or appointed office: five Republicans, five Democrats, one Green, one Libertarian, one progressive independent, one conservative independent, and one centrist independent.
Just because empire is an ugly word doesn't mean you don't live in one.