Hi Mike, welcome to Just Answer!.
It sounds like your 2.7 might be out-of-time. When you have an in and out sync signal between cam and crank, no spark, no fuel injector
delivery, it's very likely the cam and crank sensor signals aren't close enough together to make the PCM happy. Disconnecting the cam sensor solves that to a extent because the conflict is gone at that point and the PCM is programmed to run in limp-in (like you said) using only the crank sensor in this year. Barring major
complications, the crank sensor is always going to be in-time.
Timing chains don't skip on their own very often in these engines, so the most common reason for the engine being mis-timed is that work has been done recently. If the timing chains or water pump have been replaced, cylinder head removed... whatever... it's pretty likely that something happened at that time to cause your problem.
I saw an instance at the shop only a few months ago where one of the guys got a timing chain kit (complete with gears) for a 2.7 engine from this same time period and the engine would not start after installation. Bill's a very meticulous guy; it was hard for me to believe he had missed a timing mark somewhere, yet the engine would start and run fine with the cam sensor removed. It turns out that the timing chain package was mis-boxed, having a left side cam gear for an NGC engine... his was an SBEC. These are completely incompatible, with entirely different cam spacings on the gear. If your engine received a Mopar chain kit, I'd be suspicious at this point.
If you're familiar with the amount of vacuum the engine normally produces in your area, start it without the cam sensor and compare that value to what you'd expect. If vacuum is the same, cam timing is spot-on. Lower vacuum (of course) would possibly mean that things aren't quite what they should be.
Last, I'd be slightly suspicious of anything but a Mopar cam sensor if the above descriptions don't fit. My experiences with aftermarket sensors are pretty limited, but I'm seeing problems solved constantly from posts made by techs logged onto iATN (international auto technician's network), which is why I'm including this in my post. It doesn't seem plausible that an aftermarket sensor could be that bad
right out of the box, but I see it time and again. If your engine hasn't been apart... and you're using an aftermarket cam sensor... I'd try a factory unit.
Write back if you have any questions, Mike. I'd be glad to help.