Does your storm pipe drain into the municipal sewer, or does it just drain into the street (via the curb) and/or the street storm drains?
Either way, you can have a “trenchless” sewer drain run between an access pint at the sidewalk and some point near your house where the gutters discharge into the drain pipe. This is really the best way to go. Your sewer contractor will pull a polyethylene pipe through your oold clay pipe and effect the hookups on either side. You will never have to worry about root incursions again. BTW, in your area a lot of the “clay” pipe is not really “clay,” but a proprietary material called “Orangeburg” pipe. It has somewhat different characteristics, but shares the main the weaknesses of clay, namely fragility and susceptibility to root incursion.