Unfortunately I can't provide the exchange rates you're looking for, but I do think I can help clear up some of the confusion.

One thing you have to keep in mind is that these units of measure were variable from ruler to ruler even within a single dynasty. I've run into similar issues working out measurements in 斗 and 尺 before, and acquiring an old 尺-stick only confused things further since it didn't match any of the numbers I'd previously been working with.

You can almost think of tael (两 liang) as a word like "dollar" rather than a word like "gram". That is to say, it's not a constant, but rather a unit name which can and does refer to different values differently at different times, and a dollar in the US isn't the same as a dollar in Canada or Australia or Taiwan. Likewise, a tael could be of various weights and therefore various values, and the standard weight could change. For example here's a photo of various taels. You can see the shapes are variable and, presumably (though you can't tell from the photo) the weights as well.

Wikipedia being what it is, I'd wager (heh) that the wages you're seeing are from a different source than the conflicting conversion rate.