Much respect for riding that far on your commute. I always appreciate folks who are open-minded about learning new things. I think as a daily commuter I am constantly trying to figure out how to be more efficient, whether it's getting marginal gains in speed, dealing with the weather, carrying cargo, lighting and other electronics.
If you're bike is a poor fit, that's the first thing I'd address. Having a good-fitting bike will go a long way in making your ride more enjoyable and pain free.
Tires are always a compromise. So, you pick which is more important to you. I've run 25's, 28's, 32's, 35's and 38's on commutes, with more puncture protection on the wider ones, but I've had punctures equally on all of them. The difference in speed on my 40 km round trip is maybe 8 minutes. I am using 35's currently, find they are a good all round.
I don't like the panniers. Ditching them will probably make the most difference in your speed because for me they act like a pair of parachutes. I have carried heavier loads on a backpack, and I find that the position I ride with a road bike, the weight of the bag sits on my back rather than hang off my shoulder. And I have carried a backpack on longer 100+ km rides without any issues.
Hope that helps.