I'm a fourth-generation Montanan who grew up in Billings and spent the better part of my adult life in Bozeman. As such, I've driven the stretch of I-90 between Billings and Bozeman hundreds of times.
I've read the bulk of the posts on this thread and could perhaps offer some unique perspective.
Reed Point
First off, Reed Point is a very unlikely place for someone to consider a destination. I've been off the highway there maybe a total of three times in my life that didn't involve a drift boat. Reed Point is very small, and for all intents and purposes offers no "services" - gas, restaurant, or hotel for a traveler of I-90. If one needed gas, they'd be more likely to stop in Big Timber to the west that has 24/7 gas stations. Reed Point is more of an "access" to the interstate than an actual exit in the sense that there's no commerce, lighted signs, etc.
I also wouldn't read too much into the vehicle being at the post office. There really isn't a whole lot in Reed Point, and parking anywhere along its main street (Division) would be near the post office.
There are plenty of other places between Bozeman and Reed Point to get a better view of the Yellowstone, including Livingston (where A River Runs Through It was filmed) and Big Timber that are more likely to stop for such an activity. I-90 basically follows the Yellowstone from Livingston, but is further from the interstate at Reed Point than in other places.
One would not go to Reed Point to hit up a bar, restaurant, etc. A couple of the better places in Bozeman to eat and have a drink is literally right across the street from the library. Downtown Bozeman is lively and has many options for entertainment.
Direction
I hadn't seen this commented on, but I found it interesting that he was looking into jobs in Bozeman and Butte, which is to the west of Bozeman. If he was going to explore areas he might be living in, I'd expect him to have gone west on the interstate, not east.
The Yellowstone
There is one very common reason that people in that area stop and leave keys in their vehicle, and that is "shuttling." This is when a vehicle is left while a group is floating the river. However those vehicles are left at boat launches, not in the middle of town quite a walk from the river. From where he was parked, it would require crossing the frontage road and the railroad tracks to get to the river. And with as much water that was flowing at the time, it wouldn't have been conducive to a recreational or fishing float. (And obviously he didn't have a boat.)
"Stolen Car / Joy Ride"
I think this is not very likely.
If someone had taken his car from Bozeman, it seems very odd they'd leave it in Reed Point. If you were trying to "ditch" a car so you could get away after taking it, you'd be better off somewhere besides tiny Reed Point. A vehicle left there is sure to be noticed. In a parking lot with many other cars going in and out is far more likely, and that would be in Bozeman, Livingston, or Big Timber.
Thumbing a ride from Reed Point would also be quite difficult compared to other options, too.
Also, parking in front of the only two places likely to have cameras in the entire town (the gas station and Post Office) would be an odd choice.
RV Park
This is the reason for the asterisk above. The RV park is literally right across the street from the post office. This is the one place that someone would be able to get a ride out of Reed Point after leaving a vehicle in the post office parking lot.
I could envision Paul meeting someone in the library, striking up a conversation, learning they were camping in Reed Point, and offering a ride back to their RV. (Obviously, they would have had to have had a ride *to* Bozeman first.) Or perhaps he met someone and drove to Reed Point to where they were camping to hang out. Though, again, there'd have been plenty of places to sit and "shoot the sh.." (as we say in Montana) in Bozeman.
The RV Park is the most intriguing element of the entire thing to me. More than the post office (which I think is coincidental to Paul's occupation.) It's the one single destination on a Sunday evening for a traveler in Reed Point.
Interstate 90
Plenty of people traveling to Yellowstone and other places up and down I-90 who could have been there and seen something. They may not even know of Paul's disappearance as they were only vacationing, passing through, and not paying close attention to the news at the time.
That's all I can think of for the moment. If anyone has any questions about the area, I'd be happy to answer them if I can.