**Keep everything the same, but have a separate rank/mmr that is used when you play by yourself**
Same queue setup. Same queue times. Same role selection. If you're in/matched with a premade, you get your dynamic queue mmr and matches affect your dynamic queue rank. If you're with/against all solo players, you get your (new) solo mmr and your matches affect your (new) solo rank.
Everyone still lives in the same queue, so Riot gets the same continuity they desperately want, and it doesn't erode queue times. People who believe that dynamic queue compromises the competitive viability of ranked get an "uncorrupted" rank, like they desperately want. People that think premades are toxic as **** get... nothing. It solves *some*, not *all* problems.
You wouldn't be able to *guarantee* you'll play completely solo, but, since premades are typically matched against premades, odds are if you aren't in one and aren't matched with one, you won't be against one, so playing by yourself increases your odds of being in a true solo 5 v 5 game significantly.
On the technical side, it should be trivial to have clients hold two simultaneous queue positions, and remove them from the other whenever the first one is called. This might even effectively improve queue times and (although I'm no expert) should be really easy to implement.
If you think people will manipulate the system by dodging premades until they get a 5 man solo side, have the dodge penalty include prioritizing being matched w/ premades. That won't break queue times and will discourage this behavior.
Sorry to the reddit user fuzz22, who posted this exact idea 30 minutes ago on the thread that inspired me to have the same idea (albeit before I read the comments). I was lead to it here http://boards.na.leagueoflegends.com/en/c/gameplay-balance/ZEBIhuV6-a-solo-queue-and-dynamic-queue-compromise
Not trying to steal your thunder, friend :(