We need to get rid of closed primaries and first past the post voting—those lead to more partisan and ideological candidates. Replacing the electoral college with a popular vote would also help.
Elected officials are initially largely irrelevant, changes to the voting system will start with state-level voter initiatives.
Pretty much everything worth doing to voting systems aside from (1) replacing or reforming the electoral college, and (2) moving away from mandatory single-member districts in the House of Representatives, can be done entirely there in many states without elected officials being involved except in their ministerial role in certifying the results and implementing the dictated policies.
Keep in mind that our system has changed a great deal already (e.g. women and non-whites being allowed to vote), the politicians at the time benefitted greatly from how things were set up before, but those changes were still accomplished. We shouldn't give up on the idea of reform just because politicians would resist it.