Im sorry but I dont buy the line that you dont need any permits or licensed plumber. Some times you get to do a minor replacement or repair with out permits but not of this size or scope. Better get the actual code or statutes that exempt you from permits and licensing.
You will need to tap the city mainline (possibly cut/ dig up the city street…). Then run a new main all the way through your park (cutting up your road). Tap this main at each lot and set a meter for each lot. Then hook up each house all while maintaining access through the park and water to each lot.
Then last step is to disconect old main at city pipe.
Get an engineer or other professional to size the mainline and put the pipe down deep (5 to 6 feet) with lots of bedding sand (1 foot below 2 feet above). Make sure they put a tracer in as well. Lots of little details that you need a competent person to over see.
You should be able to find a local excavation company that lays mainline that will do a quality job for you. Its pretty standard work for alot of excavation.