Let me first recapitulate:
The tidal interaction in the Earth-Moon system is raising the altitude of the Moon orbit, and slowing down the Earth. There is also exchange of angular momentum. The angular momentum of the Moon is increased in the process, and there is a corresponding decrease of angular momentum of the Earth.
In the case of a black hole:
The only interaction with surrounding matter, as far as I'm aware of, is with the accretion disk of the black hole.
At large distance to the black hole the gravity from the black hole is very precisely described with the standard newtonian inverse square law of gravity. At distances like that orbital motion around the black hole is as stable as the orbits of the planets of the Solar system.
Closer to the black hole relativistic effects become significant. Long term orbital motion is still possible, but those orbits have precession (Like Mercury has precession of its orbit) The closer to the black hole, the faster that rate of precession.
So anything orbiting a black hole at that range has an increased probability of bumping into neighbours. The effect of such a bump is loss of orbital altitude. (Or the bump makes the orbit even less circular, which increases probability of bumping into neighbours.)
It's not that the black hole is actively pulling mass towards itself. It's more that over time mass that is orbiting a black hole tends to lose orbital altitude. Eventually the mass that is orbiting the black hole loses so much orbital altitude that it crosses the event horizon.
When orbiting mass crosses the event horizon the orbital angular momentum is absorbed into the overall angular momentum of the black hole.
(Many black holes have clean surroundings. All mass that was close enough to be gobbled up has already been gobbled up.)
What that means is that a black hole has only one form of gravitational interaction with surrounding matter: orbital altitude of surrounding matter decreases, and eventually that matter crosses the event horizon. (By contrast, the tidal interaction in the Earth-Moon system causes increase of Moon orbit altitude)
So in the normal course of events I don't see a process that could decrease the angular momentum of the black hole.
(Well, I suppose the following scenario is possible: a moving gas cloud meets a black hole, and the angular momentum vector of that gas cloud is in the opposite direction to the angular momentum of that black hole. If that gas cloud contracts to an accretion disk then you have an accretion disk with an angular momentum that is opposite to the angular momentum of the black hole. But that is a very contrived scenario.)
I don't see a plausible process that could make the angular momentum of a black hole come back down again.
For fun you can read up on the Penrose process