where I work, we ocassionally put stuff like this in a vibratory tumbler for post processing. it's finicky to get all the parameters just right from one material to the next, but when it works it's AMAZING.
doing that is going to create a rotary tumbler. i think for this specific object that might work totally fine, but it might be too rough for anything with fine details or sharp angles. vibratory tumblers are more likely to keep the object's overall geometry intact, whereas rotary ones will eventually sand things into kind of an ovoid shape?
as for parameters, the main ones are which grit levels for each stage, how long to run it for each stage, which tumbling medium to use, and how much water. i haven't really ironed out any general guidelines but in my experience (perhaps obviously) most plastics don't need nearly as long as most minerals.
it doesn't seem like many people have gone this route yet, so if it works out, please post about your process!
If you're in the US you could try the harbor freight route. They're still not super cheap, but this will let you feel out whether or not you'll get enough use out of one to justify buying a "nicer" one of/when the harbor freight unit breaks.