Yes, the 'hump' goes on the passenger side, some of the later years with a 2004R used a different crossmember.
This is a TH350 crossmember, note how the holes on the left don't create a line perpendicular to the angle of the crossmember tube itself.
This is a 2004R crossmember, note how the holes DO create a perpendicular line, as the crossmember goes almost straight across the frame. To get this crossmember to fit in older (I think '78-'83) cars, an extension would be needed, shown here:
Some crossmembers (I also believe early years, possibly only v6 I'm not sure) also had 'isolators' to further reduce noise/vibration transmission, they sandwiched on the top/bottom of the ends of the crossmember, the holes are close to 1" in diameter on these crossmembers (or frames, I can't remember for sure) though.
Going back and looking at pictures of my '78's frame, it appears the large holes are in the crossmember itself.