Take this for what it is worth, since I'm no expert, but...
I also have a 61 CJ5 that I'm working on right now. Mine has the Dana 25, not the 27, so I'm making the assumption that they are set up the same to handle the leaf springs. What you'll find is that both the drivers side and the passenger sides require two U bolts per spring. However, on the passenger side, one of the U bolts is larger in diameter so that it can fit over the edge of the differential housing. The other U bolt has a smaller diameter since it only has to fit over the smaller diameter axle tube. On the drivers side, you need two of the smaller diameter U bolts since they only go over the axle tube on that side. Here is a picture of my Dana 25 when I opened the diff cover. But you can see that one of the U-bolts for the spring goes over the diff housing and one goes over the axle tube. The bottom spring plate will be drilled accordingly so that the U-bolts fit through it. This is the way it is designed, so you shouldn't have any worries about serious off-roading with the U-bolt going over the diff housing in this one location.
Front Diff 1st open 2.jpg
As for the leaf spring not sitting flush on the perch, you need to make sure that the hole that the center pin fits into on the perch is clear of debris. It should sit flush as you seem to be aware. There are several holes on the bottom of the perch. Make sure you are getting the spring center bolt in the correct hole. If not in the correct hole, that might explain why it won't sit flush and also why it doesn't align with the front shackle. The shackles are designed to move, so don't be afraid to loosen the shackle to get the spring to line up.
Hope this helps. If not, the experts will be along to correct me, hopefully.