You can have mine. You just have to pull it out of my fescue lawn.
Illegal? Does some senator’s son own a lawn business or have exclusive rights to cool-season grasses?
I’d donate to any politician who outlawed new Bermuda grass installations. It’s a real nightmare here. After spending a year removing it from my front yard, a neighbor sodded his lawn with it and put a 2-foot strip between his driveway and our lawns. Thankfully, we moved two years later.
Holy 
!!! I just looked it up, and it’s actually considered a weed in NJ! WTF! I’ve never heard of that before. With your sandy soil, you’re pretty much in a tough spot.
Can you keep your Bermuda and promote it? You really don’t need seeds for it to spread. 
So do you have thin areas your trying to improve? Unless they are several feet across just bomb it with Nitrogen. The limiting factor is the narrow window of growing season you have left.
Use a balanced fertilizer like 13-13-13 if you don’t have a soil test. Apply 1 lb of nitrogen per 1,000 sq ft. The Bermuda should grow and fill in before it goes dormant. When it greens up in the spring, fertilize again to boost its growth.
Assuming the first frost is in mid to late October, there’s not enough time for new seed to establish roots before winter. Also, if you don’t know the type of Bermuda you already have, introducing a different variety might make things worse with them competing.