It feels to me (but please chime in if you disagree) that by far the biggest effect on game outcome caused by bad or good luck stems from the draw of the four starting clover tiles (the "opening draw"). But again, a solution like using the "Jason's Mode" mentioned in another thread that simply minimizes bad luck also removes some of the space in which players can demonstrate degrees of skill.
An ideal way of comparing two players might be achieved by playing 2 rounds (as we do in Tournament Mode) in which each player plays equally unlucky opening draws. So, if Player A played one "terrible" opening draw and one "not too bad", her opponent should also play one each of these. But even if we had a way of accurately judging the relative "badness" or "unluckiness" of various opening draws (hello, mathematicians!), implementing such a system would entail a number of difficulties that are left as an exercise to the reader.
My suggestion (finally): do the next best thing, and have the opponents rotate or swap their opening draws. For the sake of simplicity, say we have a 2-player Arena game in Tournament Mode with Easy Setup. The opening draw of Round 1 is identical to how we currently do it—each player's opening draw is randomly selected and placed in numerical order on their board. Let's say Player 1 draws (9, 9, 10, 10) and Player 2 draws (1, 7, 14, 20). The round is played with randomly drawn tiles as normal and, at the end of the round, Round 2 is set up such that Player 1 is receives the opening draw of (1, 7, 14, 20) and Player 2 must now play (9, 9, 10, 10). Play then proceeds with subsequent tiles again being drawn at random.
It's not perfectly equivalent because each player knows what their starting draw will be in the Round 2, but any advantage offered by this fact is mostly negated by the randomness of the tiles drawn during each round. In other words, a player may know what their opening draw will be for the next round, but that won't help them much because they don't know which tiles they will draw after the opening.
(BTW, this is the method used in duplicate bridge (wikipedia) to enable competitive ranking.)