I commute on a Crosscheck as well. With fenders, pump, heavy duty rack with 28mm tires. And like you, it is a big contrast to my Bianchi Vigorelli road bike. However, riding the Crosscheck makes me a stronger rider. When I return to the Bianchi I ride like a bat out of hell. Kind of like, was it Vince Lombardi who made his football team practice in weighted pads so they would feel lighter on gameday?
Anyway, you get the picture. Also, I would suggest installing the Mr Tuffy Tire liners with some nice tires. It really takes the worry out of the commute. Yes, a weighed down Crossheck is not ultralight, but it gives you the confidence you will arrive to your destination.