Ranked System Idea
Why don't you separate solo queue from all other queues? Have 3 ranks: Solo queue, multi queue, and ranked team queue. This way people can enjoy all queues either by themselves or with their friends or competitively. The system you have planned will cause people to have false ranks and when those that usually play with 4 others goes into queue by themselves, they will most likely underperform compared to others in the queue. Playing solo queue is one thing but queuing up against up to a premade 5 people changes the dynamic of the game. Having 3 ranks will clear up any ranked confusions and represent a more clear and meaningful rank. You stated also that if your a premade 5, you have a 95% chance of matching up with another premade 5. Why not make it 100% with 3 ranks. Also, why not 5 ranks, one for each type of queue (solo, duo, trio, etc.)? This would be too many queues and would be too much to handle in terms or management by the individual player. I think 3 is a good number to please most of the community and allow them to enjoy league as a player being able to solo queue, play with friends competitively, or climb with a team competitively.
Edit: I realize that if 4 people queue together, they wont possibly be able to get another person in the multi queue. So instead of having the system I stated above, just add a solo queue option to your new ranked system. Change the current solo queue and name it something else and keep ranked teams the way they are. This is what I intended and this would potentially solve most of the problems above.