The problem as I understand it with the solar sail idea, is that the solar sail would have to be unfurled and not tumbling to provide the acceleration described. It's a cylinder, not a flat plane, and it's acceleration is not perpendicular to it's long axis at any rate.
A solar sail is most efficient when it's unfolded in it's proper configuration and orientation, but hypothetically, there's no reason it wouldn't work, albeit less efficiently, if by some accident or malfunction, it were caught-up in it's own wires and rigging, and formed into an elongated shape like Omumamua. In that case, tumbling would actually be advantageous, because there would still always be some effect no matter what the orientation was. In other words, the worst case would be if it weren't tumbling and its horizontal axis were always aligned with the direction of the Sun.
Omumamua's radius is about 100 meters and it's estimated to be up to 1000 meters long. That's a lot of surface area for something as light as solar sail material. It's also about the only way that our science can explain how it could be accelerating. If it were some naturally occurring type of solid space rock, it would be too massive for the acceleration measured. We don't know of any natural processes that could create something with the low mass requirements, but still strong enough not to be torn apart by the tumbling ( like a loose aggregate type asteroid ).
Maybe, and this is my own notion, is that perhaps it,s some sort of space pumice? You know, all filled with holes like an Aero bar, that makes it super light, but also strong. I'm imagining a moon like Europa with underwater volcanoes where pumice forms in lower G and pressure, and is consequentially also much lighter. If a moon like that collided with another similar sized asteroid or moon, I can see how a fragment the size of Omuamua could get thrown off and escape.