I worry about your buildig the roads NOT to the city's standards. I believe your thinking is that since the roads don't fit the criteria to be a city road, that they can never accept responsibility for it and thus it must stay a private road. NOT necessarily true. Our HOA, the streets were originally private. They absolutely do NOT fit into the City code. They were designed by the county rules since it was originally in the county.
However, at original build time, the HOA shared ONE water meter. That meant the HOA was responsible for paying for the water, repairs of any leaks, and could turn the water off to any household NOT paying their dues. As you can imagine the repair bills were breaking the bank and not everyone used water equally. So the HOA decided to go to the city and get SEPARATE water meters for EACH home. The city in turn said "Yes" but ONLY if we turned our streets PUBLIC. That way they could access the road to do necessary repairs. A blessing to us. The HOA had to have a special assessment to raise $20K for the work. The roads were then turned over to the city.
When we turned the roads over, we now had to obey the city laws on our streets. They tore down our wood carved street signs and put up regular green signs. We had to cut down trees so the signs could be read in some areas. Speed signs went up. Mind you our HOA does NOT allow for signs except for For Sale/Rent. We also had to rewrite our CC&R's to integrate the changes to being public roads and separate water. That cost us 2 years and $1,500 in legal fees.
The streets were soo narrow that fire trucks and ambulances could NOT get through. This let one person who had a heart attack STUCK in the middle of the road for almost a 1/2 hour. He did pass away at the hosptial later. Our garbage often did NOT get picked up because a car was blocking the way and the truck couldn't get through. Often we would get reports of people's cars being scratched or mirror broken off if 2 cars parked on either side of the roadway. (NOT against the law). We finally had to go to the city and get one side of the road painted RED to indicate an emergency lane. We had to get special approval and a code written to allow the curbs to be painted instead of signs put up.
This is what our HOA had to face when our developer made the roadway to their "idea". You don't know what the future holds. Plan for the worst case scenerio which could be the streets turning public one day. NOT every HOA wants to stay together. If they ever do disband, the roads won't be taken care of by anyone if they are public.
As far as the HOA needing to agree to the roads NOW in your phase 2. You are the HOA at this point. You own controlling interest and represent the HOA until you turn it over. Your title may be developer but it doesn't mean that you aren't a homeowner in association with yourself.

A HOA is only formed by property owners and your the main property owner. Go to the city and find out their terms and negotiate from there. You may have to try to make an "ordinance" if you have special conditions that will allow you to keep doing what your doing.