Thanks for the quick reply. I don't have any problems with single property driveways being tagged as private, but roads such as Cinarron Lane and Sedona Lane serve multiple houses.  The wiki at https://wiki.openstreetmap.org/wiki/Key:access says private  is defined as "General public access is not allowed. Access is granted with individual permission only. Examples: A driveway with a no trespassing or keep out sign; A company parking lot for employees only." It specifies that there should be a no trespassing or keep out signage.

BTW - I live in Mount Vernon nearby a number of private roads, none are posted, and lots of people drive on the roads.

I'll leave it up to you to remove the access tag or not. Just be aware that other users could easily remove it.

On a side topic - I'm impressed with your goal to ride on every road in the area.