Could be believable if you were to feed it dark matter, it would increase the gravitational force around it and siphon a decent amount of those filaments, but i think you cant even on "believable" scale siphon billion of solar masses, how would you store it ? You would need a unbelievable giant storage system of at least "Million of solar masses" (assuming you could somewhat compact it), also that is universe destroying because if a blackhole would suck up billion of solar masses in seconds, theres nothing stopping it from consuming the whole universe , its just a matter of time.
With that out of the way, the best way i can think of would be to feed dark matter to the black hole and make it kind of a "super" black hole in order to fulfill your needs, or something different about it because all black holes cant consume billions of stars per second if you want it to be believable.In my opinion.
But i have to comeback to dark matter, its the only way i know of that could in theory be used to move masses through space without issue since they don't directly interact with it.
EDIT Since your edit provided more information, science-based tag would say that black holes don't transport matter, but ignoring that, yes it could work but unless you dump solar masses of gas in order to achieve your goals, as for a cap (Maximum amount of production) i cant be precise but i would say that more then the size of the black hole couldn't be produced in a second (you can justify with some pseudo-science that builds on the time difference that seems to occur the closer you get to black holes).