Is there anything I can do to prevent snakebites (pinch flats)?
Inflate your tires to a higher pressure. Use a pump with a pressure gauge instead of going by "feel". Check the pressure more often. The max pressure listed on the sidewall is a good starting point, but if you're already inflating to max psi, you may want to exceed it a bit.

It's likely you have a slow leak, and you're at a low inflation pressure by the time you get the snakebite. Check the tires and rims very thoroughly for sharp bits, and use water submersion to check the tube for leaks, including the valve. A fresh tube wouldn't hurt.

If your roadside inflation is with CO2 cartridges, be aware that CO2 leaks out faster, so you'll need to top off with air the next few days.

You may want to seriously consider buying a second wheelset with wider rims for urban riding with wider tires, and keep the narrow rims and tires for races and weekend rides.