It shouldn't be all that hard, really. We ban prostitution (whether we should or not is another question). It's the same principle: you can do the thing as much as you like, but you can't pay people for it.

It doesn't have to be strict. It doesn't have to be two sided. For simplicity, maybe you want to only ban the paying side. Say there can't be a post in your budget that says "influence politicians for favourable legislation" if you're an LLC. How limited liability corporations spend money is already pretty monitored, for obvious reasons, so it wouldn't be that hard.

Prostitution is an example of a ban that's almost totally ineffective, but your points about LLCs seem reasonable to this non expert.

It’s effective at its purpose, its purpose just isn’t stopping the conduct banned.

What is the purpose, then?

Marginalizing sex workers.

There's no actual benefit to that, so I'm not sure it's the reason.

There are people who benefit from it; there’s no (or negative) net social benefit, but that’s true of lots of the things that motivate laws.

Who benefits from sex workers being marginalized?

People who exploit sex workers.