What kind of incentive structure do most ransomware negotiation firms use that would actually cause them to benefit from coordination with the ransomware groups, as happened in this case? Do ransomware negotiators get paid more if they negotiate a lower price?

I believe the incentive is that they help establish a reputable connection between the ransomware group and the victim.

From what I have read in the past is that victims have no reason to trust ransomware groups and pay because what is stopping them from just demanding more money or hacking the company again. So from what I read is that ransomware companies depend on building a trust that after payment you will get your data back and he left alone.

So I believe that by working with a ransomware negotiator, a company that assumingly is a legitimate lawful business, the victim and hacker both benefit with the trust that this middleman is legit and the working history established has shown that those who pay do end up getting their data back.

TLDR: why believe a hacker that if you pay they will actually leave you alone. But a legitimate middleman with a history of dealing with these things and a proven track record can establish immediately confidence that paying will result in data recovery. So it's not about a lower price but rather a confidence you won't get screwed after paying.

Probably a percentage cut because they’re also the ones pressuring the victim to pay.