I call BS on the use of only Champions. I've run copper NGK's (LZTR4A-11, Stock No. 5306) in both my 05 Hemi LX and 06 Hemi WK for many, many thousands of miles and have never had a hint of trouble. I even run my WK with SOS coils and .060 gaps, and it runs better than it ever did. The LX gets the same treatment next, but I want to switch to the late valve covers/coils first. On the Champions, if they can't even make the same part number between dealer and aftermarket alike, I don't want any part of them. Gotta be black or silver top (or whatever) is absolute BS. I also used to work on recip. aircraft engines, and Champions were the worst, followed closely by Autolite. It appears they haven't improved much. Strange it took Chrysler a few years to figure this out too.
ISUzj, since yours is an 05, you also need to check the resistance of the spark plug wires, especially if you have over ~75K and they've never been changed. A new/relative new 3 ft. long wire should have a resistance of ~18,000 ohms or there abouts. The old rule of thumb for resistance type spark plug wires is, no more than ~10,000 ohms per foot. While plug wires are not likely your problem, it can cause misfire/stalling issues. If you have to change them, I would recommend you either purchase the Taylor Shorty wires (I currently have these on my 05), or convert to the later, no plug wire setup like I plan on doing.
Your problem could be any number of things but, since this is a new to you vehicle and it obviously hasn't had much TLC, I'd highly recommend you do a major (60K or 100K) service on the entire vehicle, including all engine sensors (MAP/Cam/Crank/O2), TB cleaning, Trans/diff/Xfer case service, EGR/PCV Valves, etc. I am sure you'll be surprised what you find. You should also consider adding a catch can (a must on the Hemi, IMO), especially if, when you do the TB cleaning, you find the intake manifold plenum very contaminated with oil. Chances are also very good that the PCM/TCM CALID flash files are no where near current. My 06 WK was 4 updates behind when I bought it back in 09. Also check the fuel pressure. My guess is once you've got the maintenance up to date, your problem will vanish.
06 GCO, Dk Khaki, QDII, Flshing Hi 3rd Bk Lt, MDS "ON" Lt, Airtab Vortex Gens, Debadged, Fumoto Drain Valve, BT Catch Can, Chopped EGR Tube, SRT8 CAI, K&N Filter, Sonnax Trans Line Press Booster, SC Tuner W/Adv Trans Tune App, DS Tuner, Cust tubular hdrs w/3 in Magnaflow/Xlerator AP Exh Sys, Bilsteins, SRT Springs/Sways, Cust Eng Cvr, SRT8 frt/rear bumpers, FRI Sidewinder Cam/6.1 valvetrain, SLP 25% UD Pulley, BBK true 90mm T-Body, SOS Ign Coils w/.060 spark plug gaps, SRT Reps with 265/45&295/40X20's.