I haven't been able to find any modeling or animation software for lower budgets that is capable of soft body dynamics.

Even if you do find one that you can afford, I can tell you from experience that animating cloth and stopping it from going into the model's body is quite a task. One that should keep you fixed to your monitor for a few days at least.

You could also try bone animation, but it won't look as good, and pretty hard to make any semblence of real motion.

Using 3dgs physics objects to control the position of vertices in a cloth model sounds like one hell of a task. I've never heard of such a thing ever being attempted, so if you are game, then I'd like to hear how you go.

I understand your frustration, there is no easy solution. I think your best bet is to get access to a high end modeling program and using its motion dynamics capabilities.