Connecting Fastrack Transition Piece To Lionel's #22972 Bascule Bridge

I am attempting to connect a fastrack transition piece to Lionel’s #22972 bascule bridge. It appears that about 1 1/2 inches would have to be cut from the track’s roadbed on both sides in order for it to fit into the three rail tubular track on the bridge’s operating end. Has anyone attempted to do this or might there be a better way of connecting the two pieces?

Now not being familiar with the bridge I may be all wet here but! How about a half section or shorter section of tubular track to the bridge, then Fastrack to that short piece. Ken