There's a much easier way to do it than that.
When you Load Locations, you can specify a different break value for each service area using field mapping. You need a column in your input data that has the break values you want (so, 10 for Facility A, 12 for Facility B, etc.). In the field mapping table in the Load Locations dialog box, there will be an entry on the left that says "Breaks_[Impedance Attribute]", where the [ImpedanceAttribute] part is filled in with whatever impedance attributes are available in your network dataset. Click in the space next to the one you want ("Breaks_Miles" or some such), and you'll get a drop-down of the fields in your input data. Select the field in your data that has the break values (10 for Facility A, 12 for Facility B, etc.). When the Facilities sublayer is created, you'll notice that the Breaks_Miles column is now filled in with the values from the field in your input data. When you solve the service area calculation on that impedance attribute, the values in this column will override the default cutoff you give it in the settings.
The "Breaks_[Impedance Attribute]" option doesn't come up when I'm loading locations into the Facilties. Do you know how to ensure that option is available?