It sure will be interesting and a happy day for all when you do finally find out what the heck is causing this stalling problem!
The only times my 99 has does that is as what has been already suggested... Crank sensor, IAC, and throttle body cleaning. If the "pick up coil" (Cam sensor) is failing, it will pretty much do same as crank sensor fail, Pcm shuts down spark n fuel =stall
Wish I could recall the reason why my PCM was replaced around 2006 or so, at that time I already had 240k or slightly more miles on it, I'd share if I could recall. I do remember that this auto electrical shop had a couple common sensors at it first then ultimately replaced the PCM which has fixed the issue ever since then. I now have nearly 320k miles on it.
At this point, personally I'd probably be willing to try n find a junkyard pcm or even pony up the $300. or so at the local o'reillys and see if that is or isn't the problem. Making sure it is warrantied and can be returned.

 

I wonder if they can test the PCM. I know they could check the older ones on OBD I systems. Fords were bad in the late 70's and early 80's with bad brain boxes. I had one Dodge where I'd converted from the Lean Burn to electronic and the box would run fine cold but it would die when hot.

 

I would imagine they have some way of testing on the bench where they Reman the units? I guess?
I went out this evening straight after arriving home, left the engine running n grabbed my infrared (Klein brand from HD) First reading was low 150's (F). 5 minutes of idle and a/c on high it held a steady 182-185! surprises me!
I bounced around checking radiator hose and radiator n alternator yada yada, Alternator was the hottest at around 200f and most everything else in that 180-185 range.
It was 93 here in north California at the time... Honestly dont know but that's my report

I'm wondering what brand sensors were bought to replace? crank sensor, tps, iac... pickup coil, ignition coil... bad connection on one or bad sensor or failing pcm?

 

yea, I'm hoping that happy day comes sooner rather than later LOL.
replaced all those sensors, no joy. we did look at local junk yard, they only had some 5.2L engine ones, and I suspect we need to be sure it is our same 3.9L for it to work, and besides, all these at the junkyard are out in the blazing Florida sun and humidity, so no way of knowing if the PCMs still work.
I did find a few places that will warranty the PCM, and one of them said they will take it back if it turns out not to fix the problem. (with a re-stock fee.)

 

Couldn't find anyone local that will test it. Dodge probably would at a gazllion $ per hour, and I feel they would want us to buy their PCM LOL.
I found an ebay store that will repair your PCM for about $100, and when they get it there they test it and give you back about $30 of that if it tests out good. They keep the whole amount if they can repair it. Free shipping there and back, but that's $70 or $100 spent and we still get our same old one back. Not the best scenario but we are considering it still.

Other places that sell a reman one range $199 to $300, it's said to be plug and play programmed with your VIN and whatever. One of them (solopcms) will charge us an extra $50 if we buy it and then discover it doesn't fix the problem. (hmm, how do we know if there's something wrong with theirs)
Anyhoo, considering that as well.
Still recovering from the catalytic converter we bought, so we'll see.

 

Well that's interesting yours was over our 160 degrees, but that was while running? We found ours still hot after the rest of everything under the hood was already cooling or cooled down. hubby doesn't remember pointing the thermo at anything else, but after a while when he came inside and told me about it, I went out and I couldn't hold my hand on it, and everything else I could reach under the hood was only warm to the touch, not hot. Mind you, we are in Florida during one of the hottest summers in history.
So what does that mean? I don't know. Maybe they do run hot.

As to brands, that's all over the place. I got parts from several different sources, some online. I did return an o2 sensor to get a Denso when advised to, and we returned the IAC for a higher priced one when we found the new one was sticking. I usually tried to choose one that was mid priced rather than cheap, and looked for warranties more than 1 year when possible.

dang.

 

Just some more food for thought...

If you want, pretty much any dodge 3.9 PCM will start and run the motor. I did this when my PCM died in Daytona and all we could find was one from a Dakota. It ran and got me home but most of the idiot lights were on---just a suggestion if you come across a free or really cheap PCM you could just for diagnostics...

Our vans do have a fuel filter. It is built into the fuel pump and non-serviceable. The only way to get a new one (other than dissecting your own pump) is to but a new one.

 

Also something that could help with getting an Bluetooth OBDII reader. Using the Torque app, you can get info an a lot of temps, readings, and values from the PCM. It will also tell you if your PCM is bad...The app in lite version is free and the reader is $25 on eBay.

I had a similar issue as you one day when my van would shut down/backfire profusely for a few seconds. After turning it off and restarting it, it seemed fine.
I was baffled like you also.
I found one day while driving in city traffic that my intake temp. sensor would read:

150-152-156-154-150--nothing--nothing-nothing --- then backfire and shutdown...

It was an intermittent sensor...changed it out and never had the issue again.

 

OK guys, fingers crossed and knocking on wood......
we got a new PCM (https://www.solopcms.com good price and great service), put it in and so far so good. Three full days without an issue, driving around as much as possible.
We have had good test drives before after replacing some part or another, so we are nervous about it, but hopefully this is the final thing.

Man, we replaced a lot of parts, but really, some of them really looked like they needed it, corrosion or carbon buildup or whatever, and one wiring harness was obviously bad; so we don't really feel like we were just throwing money away. It was just so frustrating that the symptoms kept changing and intensifying along the way. But now we have new sensors and a really good 75,000 mile tune-up

Thanks alot for all your suggestions, very helpful along the way. I will report back if any symptoms return.

 

Because of cost, I try to replace the brain box last. However, when it's bad, it's bad.