It's not his voice... I watched the first 2 vids, BoG 06 and 07, and I think it's not the voice but the style, he is trying to sing it with a calm Jazzy and Country-ish edge to it, much like he did Bad Name on SNL years ago (they did Bad Name and IML that night). It seems to be modified to sound like it did on TLFR. I blame Who Says You Can't Go Home.

Besides, the quality of that vid is pure crap so you are not getting the best of him on this. I have 80's bootlegs that sound like this but I don't think it's Jon's voice.