In my opinion the problem isn't the structure of the Senate per se, it's just that States were continually added without much consideration of how that would break the original design. There's nothing inherently wrong with the idea of a body where smaller states get to have more relative representation, the problem is allowing states with populations less than that of most major cities to exist. The simplest and least controversial way to correct that is to implement a sort of Wyoming rule to the Senate, and give D.C. and Puerto Rico statehood based on their larger populations. Maybe even bundle the Pacific territories into a third state.
The next step would be figuring out whether using Wyoming's population as a baseline even makes sense given modern demographics. However, merging small states together would probably be logistically impossible and politically unfeasible. But given the narrow margins in the Senate, you really only need 2-3 more states to get things back to sanity.