Hi Barbarossa, I wanted to point you to the road top mass transit mod, it will relieve your concern for "leaving room" for mass transit:
https://www.simtropolis.com/stex/index.cfm?id=13510
For your traffic problem, mass transit would be my first solution. Even if you have a good system now, more might help. With enough stations to cover walking distance to anywhere(that's a LOT of stations!), you can get about 80% of your traffic on MT. Keep in mind poor sims don't like the subway as much, and rich sims don't like the bus much. I plop a subway/bus stop combo at every intersection and don't worry about the cost, since fares will cover it. Finally, no matter what, some will want to drive. If you still have congestion when 80% of your sims use MT, then you simply need better roads amd avenues. Hope that helps!