a letter [...] that suggested the probability of global warming is in the same class as evolution [...] more orders of magnitude from the IPCC number than the positions of global warming skeptics.

I can only guess what letter you have in mind; perhaps this one? (Some of its signatories are Nobel laureates; most aren't.) I'll assume that's the one; let me know if I'm wrong.

It doesn't mention probability at all. The way in which it suggests global warming is in the same class as evolution is this:

But when some conclusions have been thoroughly and deeply tested, questioned, and examined, they gain the status of "well-established theories" and are often spoken of as "facts".

For instance, there is compelling scientific evidence that [here they list the age of the earth, the Big Bang, and evolution]. Even as they are overwhelmingly accepted by the scientific community, fame still awaits anyone who could show these theories to be wrong. Climate change now falls into this category: there is compelling, comprehensive, and consistent objective evidence that humans are changing the climate in ways that threaten our societies and the ecosystems on which we depend.

They don't claim that the probabilities are the same. Only that in all these cases the probability is high enough to justify saying that this is a thing that's been scientifically established.

Who would have to fund a study like this to be nonpartisan?

I don't know. Probably best not the fossil fuel industry. Probably best not any environmentalist organization. I think claims of bias on the part of government and academia are severely exaggerated, but maybe best to avoid those if only for the sake of appearances. A more pressing question, actually, is who would have to do it to be nonpartisan. You want people with demonstrated expertise, but the way you demonstrate expertise is by publishing things and as soon as anyone publishes anything related to climate change they will be labelled a partisan by people who disagree with what they wrote.

I don't have a good answer to this.

How do you make that judgement? Did you read the IPCC report [...] most of the claims that the IPCC report makes about global warming are a lot less than 99% certain.

It's not a judgement; my use of the rather noncommital word "impression" was deliberate. I make it by looking at what I see said about climate change, comparing it informally with what I think I know about climate change, and considering the consequences. It's not the result of any sort of statistical study, hence my deliberately noncommittal language. I have read chunks of the IPCC report but not the whole thing. I agree that it's good that they talk about probabilities. The terms they attach actual numerical probabilities to are used for future events; they usually don't give any numerical assessment of probability (nor any verbal assessment signifying a numerical assessment) for statements about the present and past, so I don't see any way to tell whether they regard those as "a lot less than 99% certain". They say "Where appropriate, findings are also formulated as statements of fact without using uncertainty qualifiers", which I take to mean that when they do that they mean there's no uncertainty to speak of.

Here are a few extracts from the AR5 "synthesis report".

Warming of the climate system is unequivocal [...] it is virtually certain [GJM: this is their term for >99%] that globally the troposphere has warmed and the lower stratosphere has cooled since the mid-20th century [...] It is virtually certain that the upper ocean (0-700m) warmed from 1971 to 2010 [...] Human influence [...] is extremely likely [GJM this is their term for 95-100%] to have been the dominant cause of the observed warming since the mid-20th century.

The key "headline" claims that distinguish the "global warming" from "not global warming" positions are "virtually certain"; attribution to human activities is "extremely likely" (and I have the strong impression that they are being deliberately overcautious about this one; note, e.g., that they say the best estimates for how much warming known human activity should have caused and the best estimates for how much warming there has actually been are pretty much equal).