Wow, Top Spin....looks like a touched a nerve. I have no agenda, just a lot of experience with tennis ball machines. And sorry if I have a brand preference. Most do.
You make some valid points regarding draining batteries. The biggest enemy of SLA batteries is to be completely discharged. But I still think you are in the minority based on the amount of time you are on the court with a machine. If the majority of ball machine users played for 4 hrs or drained the battery like you do, ball machine companies would quickly see the current 18Ah SLA batteries they use as inadequate.
I don't quite understand why an external battery pack is such a bad option, esp. given the limited alternatives. But good luck to you finding one.