Bummer to hear about this Fitz! I'm kind of stumped because I know the feeling you're describing here... I've even had it happen with cars before. The grooves sort of grab you and pull from from side to side requiring more strength and attention for steering.
I think the larger balloon tires would actually decrease the impact of grooves or bumps in the road vs. narrower road tires. To me, it seems like thinner tires would wedge into the channels even more and send harsher feedback up through the wheel and fork.
The most obvious change you could make would be with the tires because they interface directly with the road. To me, larger seems better for dealing with this kind of thing and Pedego does make the
super wide Trail Traker wheels and tires but they are much less efficient and probably aren't compatible with your City Commuter. I'll Google around and see if I can find out how cars deal with this issue. Upon further inspection and recollection of my own City Commuter I realized the tread pattern is linear and parallel with the direction of travel as shown in the image below. Maybe if you get flatter tires or ones with knobby tread instead of striped you'll experience less pull.
Check out the tread on the IZIP Zuma, it's more perpendicular to the direction of travel and might reduce the impact of grooves. There are lots of other options out there, bummer you'll have to spend more but it might solve the issue. Be sure to get some with Kevlar lining or use some good tubes as usual.
Here are a few tires I found on Amazon that should fit the 700C tires on the City Commuter. I double checked the documentation and your bike currently uses Schwalbe Fat Frank Balloon Suspension Tires with Kevlar at 28" x 2.00"
