Well, I can surely feel your pain on this one!! I have a Jeep in my shop right now having very similar issues. Here is what I have learned over the past week of pure hell with this engine:
Your problem is most likely in the timing chain. If you made the unfortunate mistake that I did and installed an aftermarket timing component kit you will need to have the factory sprockets put back in place. There are 2 different tone rings for the cam sensor. One is for the Jtec system and one is for the NGC system.
An engine with the Jtec will have a 3 connector PCM (engine computer). NGC will have a 4 connector PCM. The cam tone wheels have different window patterns. So, you could have the totally wrong sprocket for the right hand head cam. However, I also have discovered that my kit had a sprocket that looked pretty much identical to the original factory one but still did not work properly.
Plus, in the long process of dealing with this I have also come to the conclusion that the idler sprocket may not be completely lined up the same as the OE one is. With the aftermarket timing chain parts installed and the colored links placed at the corresponding marks on the sprockets, my engine had 150 psi compression on the right head and 175 on the left head. Moving the right had sprocket with the tone wheel one tooth clockwise (when looking at the front of the engine) the compression came up to 175 on the right head. However, this set the timing out of whack also and has caused the coils to all fire at once and blow the ASD relay fuse.
So, the only solution is to use the factory timing sprockets and use extra care to set the timing correctly. I don't know how to post the setup pic but any pro shop will have access to that info.
I noticed that when the right cam sprocket is set correctly, the cam sensor should be lined up with about half of one of the tone wheel windows (it will be a 2 window set that is close to the end of the sensor). When I had the right cam advanced one tooth, the sensor end was lined up with a solid part of the tone wheel, just past this 2 window set.
If the timing in your engine has been off already, the ASD fuse is likely blown. Make sure they check that. My engine was also setting ignition primary codes once it ran with the OE tone wheel installed but advanced one tooth.
I really hope this helps! The timing setup on this engine is really poorly designed. The procedure to line everything up is too ambiguous. The manual says the v8 symbol on the cam sprockets is supposed to be at 12 o'clock when the crank is at #1 top dead center. However, they don't seem to really be at 12 o'clock no matter what you do. They are either a little bit before or a little bit after. And, in this case I believe the right cam should be a little before 12 and the left should be a little after.
I have taken the front cover off of this POS 3 times now and have to do it again tomorrow! I would have had zero problems if I had used all OE parts for the timing kit. Hard, expensive lesson learned! Good luck and let us know the outcome.