I've never used an inversion table, so I can't comment on it. But I'm not sure I like the idea of being upside down for any length of time; I heard to can be risky.
In my own case, I bought a Perfect Fitness Multi-Gym doorway pull-up bar expressly for my lower back and (left) shoulder, which I injured outside the gym. I only use it for dead hangs since I work out at the gym.
Since posting my earlier comment, I found this site citing the benefits of a dead hang:
https://theworkoutdigest.com/dead-hang-exercise/
Seems like a pretty good multi-purpose alternative, no? At least for the lower back if perhaps not quite so much the upper.