"You can't do much to change the total compensation of elected officials - what you can change is the share that doesn't have to come from corruption."
Yes, you can do something, *IF* you can get the legislation passed. Granted, that is sometimes a rather large hurdle. But in principle, it's actually very simple.
First off -- and related to both the former and latter parts of your sentence -- you can limit contributions from ANY entity other than a voting-eligible citizen, to ZERO. Both campaign and other contributions. Half the problem is solved right there. Make it a crime for both parties involved, and give it teeth.
Second, limit the TOTAL political contributions from any of those individual voters, annually, to a reasonable percentage -- say, maybe 10% or even much less -- of the MEDIAN U.S. annual income. That solves most of the problem of rich people having more influence. Poor people can easily outgun them with a little bit of effort and sacrifice. It may not be ideal, but it's WORLDS better, and far more FAIR, than what we have now.