I have had to replace several of these engines due to loose valve seats/bad valves. They can loose just enough compression to run weird but not have a full time dead miss. Run a leakdown test or put compressed air in to each cylinder, one at a time at TDC. You will hear hissing out of the intake or exhaust on the bad cylinder(s). You could just do the head(s), but these engines are so common and cheap that it is MUCH faster and less expensive to just swap if you find this problem.
As mentioned above, do a compression and leak down test to see the variables between the cylinders. Is your misfire noticeable at idle and the goes away once you accelerate? Do you hear a light ticking sound at idle or light acceleration? The reason I'm asking is that my '05 Grand Caravan did the same thing at around 120k miles. It ended up needing a cam & lifters. The lobe on #1 wore down the most, therefore the valves were not opening and closing properly. The cam lobes were badly pitted & the roller part of the lifters actually had a divot wore into them from the cam. My buddy is a life long Chrysler tech and mine was only the 3rd one of these he ever saw. The 1st one was a warranty and Chrysler replaced the short block, saying it was a line bore issue. Oddly, the 3.3 is the same style engine and has never had that issue. The 3.8 is a 60 degree engine so the heads need to come off to do the cam and lifters. My van is a nice, rust free, loaded model so it was worth me doing the job. That was 30k miles ago and it still runs strong and smooth. I had the heads gone over and installed a new timing chain and gear set as well. Sorry to be the bearer of bad news. I hope your problem isn't as deep as mine was but it is a possibility. Good luck.
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