Just repeal the 17th amendment. That would fix most of the issues because it would change things back to state legislatures appointing and sending senators. Before the 17 amendment senators had an average time of around 4 years in DC. That's shorted than a full term. After the amendment the average time became what it is now, which is something like 20 years.

Shorter terms, and the possibility to be called back early and replaced made it harder for senators to be bought off. It also made them more accountable to their states.