Got rebuttals for any of my criticisms about the methodology?
I do!
I think the importance of American bias is overstated. What matters is that they're transparent about it. That bias also impacts the least important thing they track. People often fixate on that metric when it has little impact on other metrics or on the most important question for this community: 'how likely is it that this source is telling the truth?' Left and right are relative terms that change drastically over time and space. They even mean different things at local and national levels within the same country. It's not really an MBFC problem, it's a the-world-is-complicated problem that isn't easily solved. And it's not like they're listing far-right publications as far-left. Complaints are almost always like, "this source is center not center-left!" It's small problems in the murky middle that shouldn't be surprising or unexpected.
It's also capturing something that happens more at the extremes where publications have additional goals beyond news reporting. Ignoring Fox's problem with facts/misinfo, it doesn't really bother me that they're penalized for wanting to both report the news and promote a right-wing agenda. Promoting an agenda and telling the truth are often in conflict (note Fox's problem with facts/misinfo). CBC News, for example, probably should have a slightly higher score for having no agenda beyond news reporting.
It might matter more if it impacted the other metrics, but it doesn't really. Based on MBFC's methodology, it's actually impossible for editorial bias alone to impact the credibility rating without having additional problems -- you can lose a max 2 points for bias, but must lose 5 to be rated "medium credibility". I don't know why FAIR is rated highly factual (and I'd love for them to be a bit more transparent about it) but criticizing bias leading to them being rated both highly factual and highly credible feels like less than a death blow. If it's a problem, it seems like a relatively small one.
MBFC also isn't an outlier compared to other organizations. This study looked at 6 bias-monitoring organizations and found them basically in consensus across thousands of news sites. If they had a huge problem with bias, it'd show in that research.
On top of that, none of this impacts this community at all. It could be a problem if the standard here was 'highest' ratings exclusively, but it isn't. And no one's proposing that it should be. I post stories from the Guardian regularly without a problem and they're rated mixed factual and medium credibility for failing a bunch of fact checks, mostly in op-ed (And I think the Guardian is a great, paywall-less paper that should fact check a bit better).
So I think the things you point out are well buffered by their methodology and by not using the site in a terrible, draconian way.