Its not really too late to seed for rye, but you may freeze newbie growing plants if we get a cold snap before they are established. Risk factor but the seed should germinate, especially if you can catch a few sunny warmer days in a row and keep the soil moist. This grass dies out in the heat, choose perennial rye as it is less agressive and not as thick. No, its not really perennial here.
Bermuda seed, on the other hand, won't germinate in cold soils. The birds will appreciate the winter diet, but you should probably just hang in there for now. You shouldnt' need to seed each year with bermuda, unless you don't have good coverage. But if it is in full sun and decent soil, it grows like the weed I feel it is.
(i'm a flower gardener with little use for turf unless there is a ball involved.)