I used a drill to plant some rye a few years ago and had a good stand.  The problem with broadcasting the seed on hard dry ground as you describe, even with a rain the seed may or may not get some soil covering it.

I would use a drill.  Or if you want to broadcast, at least pull some sort of drag over it after broadcasting. I have had some good stands pulling a Wingfield harrow over broadcast seed when I am trying to get some cover on a winter sacrifice area etc.  Not as good as a drill but better than not doing anything to incorporate/cover the seed. jmho.

Good luck.

Jim at Dawn