Optionality: A DQ Solution
What if we introduced a system of exclusion. That is, a check box which players can select if, within DQ, they ONLY want to play against solos.
The queue itself doesn't have to change, it's still one queue to rule them all.
For example, most often I play DQ solo, but occasionally I do with premades. Overall, however, I don't mind at all if I'm with another group or not. But a lot of people clearly do, so what if you allowed for an "option" to "opt out" of joining a premade group? In low ELO you have plenty of players such that queue times would survive just fine, I imagine.