If your main goal is to replace someone else's content, this probably isn't the best way to go about it. Commercial shortwave stations are businesses, and religious broadcasters are their biggest customers. I would go so far as to say stations like WRMI, WWCR, and WBCQ probably couldn't stay in business today if religious broadcasters weren't purchasing large blocks of time and providing a steady revenue stream.
If you have a cool idea for a show, and you just want to get it on the air, contact a couple stations and ask. The worst they can do is turn you down. A few years ago, when they didn't have a full slate of programming, WBCQ made social media posts to the effect that you could purchase time on a one-off basis, and they would use it to fill unpurchased airtime or when they had an unscheduled opening. You just wouldn't know ahead of time when your show would play. I haven't seen anything about this recently, but they still seem to have a couple openings in their schedule.
There is absolutely no way you're going to "kick off some other program" that has already paid for airtime. If a station will sell you time on a non-recurring basis, it will be during be during an opening in their schedule.
As for music licensing, the license fees most radio stations pay to ASCAP, BMI, and SESAC are based on a percentage of the station's revenue. If the station already plays commercial music, I would expect the music licensing to be baked into the price of the airtime. Again, it's only something the salesperson at the station itself can answer for sure.