Synthetic oil will prevent gunk from forming and very very very slowly remove any old gunk.
As far as the dead 2.7, your best bet is to try to work with your dealer if that fails send letters to ALL and ANY Dodge/DaimlerChrysler executives you can. Complaint letters generaly work and VERY well if you mange to get it in the hands of some big boss.
If your dealer doesn't do much of anything, and they probably won't. Warranty is out so you're out of luck as far as the dealer is concerned.
Try letters to higher ups, like the owner of the dealership. Make it very nice, faithfull Dodge customer yadda yadda, love my car, treated it like a baby, just out of warranty and it broke.
This isn't a step by step process, write letters to Dodge execs right now, even if the dealer is taking care of the problem or claiming to it's good to have back up plans. Just don't take "Sorry you're out of warranty" as an answer. You can probably find high level points of contact in their financial reports etc. Don't bother with the "common" means of contact (the PR
department is there to ignore you).
As far as the 2.7 engine, well it's got heat issues, it tends to overheat at times and thus burn oil resulting in gunk. Gunk can strike generaly after 30k, most often at 40-60k.
Most people with gunk problems after warranty (even on extended warranty) get screwed with gunk. Reason is that extended warranty doesn't cover "negligence" and gunk is seen as proof of late oil chagnes despite the fact that 2.7 burns oil regularly.
If you have a 2.7 now syntethic oil will almost guanrantee that you will not have a gunk issue. Synthetic oil does not oxidize at anywhere near the same rate as natural oil. More importantly it slowly loosens the gunk that's already formed and removes it.
Quick way to check for gunk is to look at your oilcap, it should not have anything slimey or sticky.
If you wonder why I know so much about the 2.7 it's cause I was in the market for a Chrysler Concorde recently and I tend to do my research. I ended up getting an LXi just to avoid the 2.7.
Also, I'm fairly sure that there are plans by some group to sue DaimlerChrysler for the engine issues, look it up on google.