How about electing the Senators by a committee of 25 people chosen at random.
Hmmmmm? The only problem with that is the makeup of the 25. You couldn't choose them at random - because you might end up with 25 democrats and then where would you be .. you'd have 100 democrats in the senate. I cannot imagine how horrible that would be.
I still say - it should be an appointment by the Gov of each state - a one-time 6-yr appt. That would keep fresh blood flowing into the senate every six years.
If they only had 6 years to accomplish things - maybe we'd get more done.