A lot of the public and semi-public handwringing has been over the subject of having "benches." When there's no one else capable of doing, say, Program AV for the con, do you hire the rapist (Arisia's answer three years running, it turns out, has been "yes")? When no one else is running for President of the corporation (or when the person running against the problematic person has values you don't agree with), what happens? Long-term, obviously, the con needs to build a bench, train new people, etc. This part's generally obvious and agreed on by everyone, and there are good proposals about how to do it (mentoring, apprenticeships, etc) in lots of places. But that's the long-term solution.
Short-term, though, there are four choices if you lack a bench and don't have someone who can replace the person you need to get rid of:
Choice one is to actually run the con with the dangerous person on board. This is the decision Arisia chose to make (without making the actual danger itself known to members or most staff), and that other cons have done in previous years (see Wiscon/Frenkel). I do not consider it the right one, and it's clear that almost no one else does. Note that as a general rule, only a handful of people on staff at a cone actually will know this is happening (so while I use the blanket terms "Arisia" and "Wiscon," it's likely a small subset of folks near the top of the boards).
Choice two is to suck it up and deal without them. Yes, that means someone else is going to have to do more work, and work they're not qualified for and have to learn quickly. It means some aspect of the con will be weaker than intended. It might even mean that something doesn't take place (if only one person can run the masquerade or a certain special event, that event might not happen). It sucks, but it also ensures that the dangerous person isn't a part of the con. It's NOT, to be clear, sustainable; asking folks to work beyond their means is something that can be justified in an emergency, but not as a regular event. It's also something that some cons can handle better than others (bigger ones usually have more staff to spread around; smaller ones might have a looser structure or fewer technical requirements that require skillsets).
Choice three is to recruit a replacement. If the only person qualified and willing to handle tax issues for the dealers at the con is also someone so toxic that they're on the "do not hire" list for your con, you probably can't ask a Green Room staffer to pick up that ball. So you have to start looking at who has the skillset elsewhere. Look at the org charts of other cons, local and otherwise. Ping the people who do the jobs there and at places like Worldcon to see if A) it's something they can do, and B) if they know others who might be capable of the job. Shockingly, skilled people often know other skilled people. And if you have to, see if money can help. You may not be able to pay someone, per se, but if you can offer a comp, or even a room comp for a night or two, or something, it's money well-spent (that said, also set expectations; this is money being spent to deal with an emergency, and not something that should be expected every time).
And choice four is the nuclear one: If you genuinely can't run the con without a rapist on staff, maybe you shouldn't run the con. That can mean any of A) You personally should not run the con (because maybe someone else can find a replacement), B) the con itself should skip a year to give you more time to find a replacement, or C) the con should end. Really. It's not an ideal choice, but if you find yourself incapable of finding a replacement, or running the event without the person, your choices come down to either letting a known predator have power within the con, or not running. If you really think that the running the con with the dangerous person on staff is the better choice, you're part of the problem.