After I had cleaned my firing pin channel, which was carbon-fouled, the roll pin that holds the firing pin in place started to mushroom when I reinstalled it.

Is there a substitute that I can get that won't do that?

Thanks

Use a roll pin punch. Additionally, some folks will lightly bevel the insert end to ease the task. Tiny bit of lube can help too. My go to for quality pins, springs, more is McMaster-Carr

Thanks, bamashooter.

Which of the McMaster-Carr pin types would you recommend for the 15-22's roll pin subsitution?

Just bite the bullet and buy the factory replacement. Available at Midwest Gun Supply, Numrich, and probably others.

There are roll pins, spring pins, etc. Whichever pin is a compatible replacement. As suggested by Kp321, you'll be fine with a "replacement" pin from a reputable retailer. If not terribly expensive, I'd recommend 2-3 pins.