Those most qualified to be "League Commissioner" would be most vulnerable to accusations of bias. If we were going to do it, Isaac would probably be the best choice by far; he is fairly conservative, but usually conservatively fair, and the level of party involvement informing his personal interest means he is probably at least as knowledgeable as anyone else here.

Regardless, I have too many eye of the beholder arguments that get nasty too often to sign on for something like that. Sure, I can think of a few other positions.

Designated Attack Dog: Almost EXCLUSIVELY a mudslinger, at EVERYONE on the other side, to help his whole party; Cantor has done a good job the past year or so. Gains 1 point for every 2 polling points the opposing party and/or their highest ranked office holder lose.

Fundraiser in Chief: Speaks for itself; a pol who excels at raking in campaign money from individuals, businesses and PACs, for himself and the party. Gains 1 point for every $1 million raised either by personal appeals or events sponsored by the FiC, though nowadays $10 million might be better.

Scandal Magnet: Pols whose great charisma, knowledge, experience and fundraising only just keep them in the game (or not) despite their trail of slime. Gains 1 point for every drop in the polls within a week of a national story about a personal and/or professional scandal.

Team Manager: Leaders like the POTUS, Speaker, Majority Leaders, Whips, but also the R/D Congressional Committee Chairmen. Gains 1 point for every 2 points their party or its leaders gain in polling. Alternatively, gains 2 points for every Congressional seat netted.

Truth Challenger: Defiant denier of reality. Gains 1 point every time they are caught making a demonstrably false policty statement.

That is just off the top of my head, and other metrics might be better for each position, but I would not touch running it with a ten foot pole, and still think it would be an unprecedented crapstorm.