He used an axis (and mesa transatlantic) on The Looking Glass and Along for the Ride.
edit: from JP:
There are two big differences, one is the guitar. That's the one song on the album on which I didn't use my signature guitar, I used a Music Man Axis. My tech Maddi [Matt 'Maddi' Schieferstein] had his Music Man at the studio and it was the Eddie Van Halen model from back when Eddie endorsed Music Man guitars. It has like a 12-inch radius, 22 frets, Floyd Rose, but every time Maddi would look at me I was playing that guitar. So I called up Music Man who have been so good to me over the years, and they made me one, the difference being they routed the body so the bar could pull back.
"So they sent it to me and I really wanted to use it on the album
Edit 2: I also remember a jp13 with a roasted maple neck and a floyd, John used it for the solo of Surrender to Reason I think. If I remember correctly, the jp13 has an axis neck profil , 22 frets. There is pics but I can't find them.