The production clouds only the ghost notes in the hi-hat and rides (although these are quite noticeable in Surrender to Reason, The Looking Glass and A Life Left Behind). The other Mangini-isms are not muddied by the production. The most noticeable is his crisp bass drum playing, where he is very playful, compared to the snare where he plays simple downbeats. Outside DT, good examples of his bass drum style is in Venice Burning with Mulmuzzler, the whole Elements of Persuasion album of JLB, and Thanks for Nothing with Tribe of Judah. In the DT songs, best examples are in Bridges in the Sky and The Path that Divides, especially the "rap" part. Another very noticeable Mangini style is going up and down the scale in unison with the other instruments.
A lot of Mangini-isms, though, are subtle. It's his style to blend in the music. For example, hearing him play two different patterns at once takes some being used to. One of my favorites is at the start of OTBOA, where his bass and snare is doing the rhythm and bass guitar pattern, while the cymbals is doing the keyboard pattern. You won't notice it until you listen to the patterns separately. Then there's The Walking Shadow, where the crash is doing an extended meter in sync with the guitar while the snare is following Labrie's lines that is on a decreasing time signature. The one handed drum rolls only become apparent when you realize that you are still hearing a constant cymbal hit on the downbeat while there is a drum roll
. Then there are the crazy things like doing two snare rolls at the same time to mimic a marching band in Astonishing.
So Mangini-isms are all over once you learn to hear them. For me, a good sampler would be OTBOA, LNF, BITS, STR, IT, A Life Left Behind, The Path that Divides and The Walking Shadow. You would get the Mangini style with these songs.