The reality is that the people that smoke past you might only get to their destination a few minutes sooner than you if they were going to the same place.

If you have a lot of stop lights, it's not going to matter too much what you ride, that's going to be the limiting factor. If you have some decent stretches of open road, then a combination of changes could knock off 5 minutes. 10 minutes might be harder to achieve consistently and it really depends on how hard you're willing to work.

I really doubt a road bike or clipless pedals alone would make more than a few minutes difference. You'll have to ride faster. Now, just getting on a road bike might help. Sometimes it's just an attitude thing.

Regardless of your fitness level, cycling is a different activity. There are all sorts of ways to train yourself to go faster. Ultimately (short of an e-bike), if you want to go much faster, that's what I think it's going to take.

Think about it for a moment. At any given point during your commute, you can choose to go faster, right? So the key is to train your body to be able to maintain a faster pace for longer periods of time. How do you do that? Well, you ride faster.
Do a little research into interval training. That will help.

Also a little competition can help, even if it's with yourself. "Strava" and other smart phone apps like it automatically keeps a history of your times. You can see how you're doing compared to your personal best and the best rides of other people on the same stretches.