Yes, $350 a day is a fair number for a CE340 in the midwest. Since there is no benefits, maybe you can negotiate a minimum amount of days per month(whether you fly or not) say 6 or 8 day's of pay?
When I got furloughed, I flew a CE340 in the North East for 400 a day, however, I failed to negotiate a set minumum number a day's per month. My bad, in the long run.
Also, make it clear, that you can work for other people. Otherwise you are considered an "employee" which opens up a can worms.
Good Luck