If you can afford it, and you want to, try seeding both warm and cools. I see it working for other people.I have thought about both seasons but only have though you can plant certain seeds and certain times of the year.
The warm season will wait on the right conditions and sprout. Assuming birds don't eat the seed. Definitely only drill with both types. Broadcasting leaves them vulnerable as they wait to come up.
My 2 cents.