Make one ride a week a real training ride. Ride it like a road race. Try to keep a solid race pace during the entire commute. Recover on the trip home.

Mine is usually Monday when I am feeling stronger. My commute is 20 round trip and I have to get over a ridge at 800'. I start at 200' going to work and 20' going home.

The least you could do is keep your gearing moderate for me that's 39/23 or 39/20. I run a 53/39 with a 12/25 rear.

Good luck to you. Sounds like your training well. Maybe step to Cat4 for a better challenge?