The problem with the deal now goes beyond Mauer's complete power outage, he quite demonstrably is no longer a top-level defensive catcher, which coupled with his apparent unpopularity with the pitching staff makes him more a liability at the position
Really? Where do you get this information, especially the second part?
Beyond that, a couple of things. I appreciate that you went to the effort to use data to try and back up your initial claims. I should add that I don't think Mauer is performing at the value of his contract this season. There's a major flaw in the initial question, as hinted at by others: Hitting order is not a position and does not have much to do with player value. If we shift Mauer to the 8th or 9th spot, he's suddenly far more valuable by that logic. Additionally, many of the players you list are under team control, so including contracts of non-negotiated salaries is somewhat misleading. Admittedly, it would do little to help Mauer in this case anyway in this analysis.
I don't think anyone would argue this is going to be a good contract. However, I think a lot of people think it's worse than it actually is because of the way people value certain stats over others. In fact, Nightengale's evaluation falls prey to exactly that, quoting only average and HR. Again, I'm not arguing here that Mauer is playing at the value of his contract, but I'm pointing out that what is examined is not always indicative of complete value.
Here are a couple of other metrics: (Note these assume his current numbers stand for the entire season, which I think is actually a conservative estimate. They also assume he continues to play half his games at catcher. If he plays more C, these numbers increase. If not, they will likely decrease unless he ends up being a lights out defensive player at 1B).
-WAR: Mauer's WAR is currently .9, according to http://www.baseball-reference.com
. If he continues with the same numbers he'll end the season with a 4.5 WAR, not a great number, but one that puts him as borderline all-star.
-WOBA: Again from Fangraphs, is .352. well above average.
/ gives player value in a monetary amount. A nice item to look at in exactly this kind of discussion. Mauer's value through the season so far is $3.7M. Multiply that out and you $18.5M.
To be certain, these are not $23M numbers, nor are they even good for Joe. However, I was actually surprised by, relatively, how good they were. Sure, some will dismiss them for whatever reasons, but these are, imo, representative of his actual holistic current value without nitpicking and choosing specific individual numbers, and I'm actually expecting all of them to improve as the season goes on.