Now that we have flex q, why don't you make solo q... a true solo ?
Now that you can play as 1-2-3-5 man party in flex q, it would be pretty self explanatory that solo q would be pure solo. It would benefit both q's, IMO. Solo would be pretty competitive and rewarding to get your division, and flex q would get 2 man parties to complement the 3 man parties. Boom, everybody's happy.