If you are leaving San Diego about September 1st and do typical mileage, you will end up in Las Cruces about September 17th. It will be very hot in places, i.e. the AVERAGE high temp for Phoenix is 102 on September 10th. Once you gain altitude it cools off pretty quickly, i.e. Silver City's average on Sept 17th is the mid/upper 80s. Still warm but not near as bad as 100+. Getting from there to Tulsa via Alamogordo, Roswell, Clovis, Amarillo, Route 66 (loosely), to Tulsa is about 860 based on a route I developed a few years ago thinking about a similar trip. That would put you into Tulsa about October 1st. Assuming you connect up in Girard, KS on the TransAm and stay on until the Blue Ridge Parkway, you are adding approximately 1,500 miles or 27 days. To get to NYC, add 400 miles or 8 days which is arriving in early to mid-November. If you are comfortable with the weather, that is quite doable.
You should note that between Roswell and Portales, NM there is not too much other than a conv store. If you are camping and willing to eat cold food for a few days (assuming you are eating out), again it is doable. There are services between Las Cruces and Roswell fairly evenly spaced, and from Clovis eastward. This is based on camping not motels. Once you get to Oklahoma, even motels will be doable but you may have to ride short or long days which could alter the dates/times above.
If you can give as much detailed info as possibly, the community could help you better.