The major ISPs have a ridiculous amount of resources and are free to publish datasets answering this question at any moment. In fact, I'd be astounded if they don't already have this data, both for themselves and for their competitors. So until ISPs share that data, I'm terminally unsympathetic to any sort of bias in the public record on this particular topic.
Also, the selection of left-leaning people doing publicly accessible research is, AFAICT, a self-selection. The problem isn't that our institutions are biased, but that conservatives (in general) choose not to pursue scientific careers in the same numbers as liberals. This suggests a fundamental limit to your proposed solution because there aren't enough "heterodox" collaborators to ensure viewpoint diversity. One of the studies published on the website you mentioned even suggests this underlying cause.
Also, I'll note that in the vast majority of academia, internal politics (what research methodologies, maths, etc. someone likes to use) are far more of a problem than external politics (of the sort you'd typically call "politics" in general conversation). E.g. I'm not at all worried about "liberal bias" in physics or chemistry or CS; if it's a problem at all, then it's a minor one compared to other problems.
Also, the selection of left-leaning people doing publicly accessible research is, AFAICT, a self-selection. The problem isn't that our institutions are biased, but that conservatives (in general) choose not to pursue scientific careers in the same numbers as liberals. This suggests a fundamental limit to your proposed solution because there aren't enough "heterodox" collaborators to ensure viewpoint diversity. One of the studies published on the website you mentioned even suggests this underlying cause.
Also, I'll note that in the vast majority of academia, internal politics (what research methodologies, maths, etc. someone likes to use) are far more of a problem than external politics (of the sort you'd typically call "politics" in general conversation). E.g. I'm not at all worried about "liberal bias" in physics or chemistry or CS; if it's a problem at all, then it's a minor one compared to other problems.