Part time would just give them more out-of-office time to do under-the-table and good-ole-boy deals.
The solution is not to make them part time.
The solution is to make them term limited and add restrictions such as:
they cannot seek another elective office unless they resign any currently held elective office.
Story today in the Bergen Record about state legislators working part time and then also working elsewhere.
http://www.northjersey.com/news/opinions/110060134_A_cry_from_an_unlikely_corner_on_dual_jobs.html
It sounds like you want term limits, and ankle bracelets while they ARE serving. Just kiddin’ ya!! Jindal agrees with the term limits.