That effect you like - that I'm hearing has been automated. ie. the returns for the reverb has been automated manually to avoid the muddiness as appose to if it were to be statically placed that loud throughout the entire mix.
If you eq the reverb by taking out the lower mids you'll loose the warmth of the reverb you're after. Removing the mud in the Reverb isn't by eq sometimes, if you have a multiband setting to control the decay in the lower mids, try winding it back a tad according to taste.
Also, there's a delay on the reverb that is in sync with the BPM of the song.
Latter in the song 2:43 + the delay is more prominent. Notice how the mix engineer rides the echo/reverb so you hear it at parts to give the illusion of something more.
Mixing Engineer www.acoosticzoo.com