One way to start is to remove the opportunity to become fabulously wealthy while earning "only" $170,000 per year in a costly environment. Start with TERM LIMITS. Get them out before their networks can become entrenched. Require that all political donations be ANONYMOUS; you can't sell influence if you don't know who is buying. Americans should be permitted to donate to any party or candidate in any amount the choose; that is FREEDOM. But when it become tit-for-tat bribery it is criminal. Force lobbyists to argue their positions on the MERITS, not on "we gave you..."
Finally, make congress subject to all laws and regulations which apply to the general public, eliminating the insider trading with which they enrich themselves.
I agree with everything you said in your post. Term limits is a must. It would be the most effective way to reduce Federal power and curruption. I would even agree to a very large pay raise for Congress if they closed all other loopholes of income.