Hi manof25,
I think you may be using the wrong tag to denote street parking. The parking=* tag is to be used on parking lots to denote the type of parking (e.g. surface, rooftop, underground, etc.). It should not be used on roadways.

For roadways, consider the parking:left, parking:right, and parking:both tags to denote the presence of parking on either side of the street. See the wiki below for reference on types of values that can be used for this tag.
https://wiki.openstreetmap.org/wiki/Street_parking#Parking_position

You may also use tags like parking:both:orientation to denote the configuration of parking spaces in a standardized manner that data consumers can use. https://wiki.openstreetmap.org/wiki/Key:parking:both:orientation

Both of the aforementioned tags are built into the iD framework, and you can more conveniently access them while editing a roadway via the tagging field drop-down menu by selecting "Parking" and "Parking Orientation" respectively.

The descriptive parking values you currently provide (e.g. "Mo-Fr school run-time single yellow lines") can be added as a note on the roadway using the note=* tag.