I have a feeling that this guy may have been an Army veteran of the Korean War. Another possibility is that he had been a boy scout once. The reasons are that he seemed to be traveling fairly light and was intent on camping in the open. He also was familiar with firearms to the point that he owned a highpower rifle.
Other reasons that I suspect he may have been a Veteran are that he was an older guy going to college (possibly), and there were many Veterans going through school on the GI Bill in the 1950's. Also, if he was drawing a pension for a service related disability, he would have had some spending money without having to work a job.
I have not seen all of his camping equipment, but what has been described, and what I have seen, is not military issue type of gear. It is more like what boy scouts had back in the 1950's.
The amount of ammunition would have been about 60 rounds, given that there are normally 20 rounds per box. My feeling is that he was simply taking his hunting rifle and ammunition home with him, after using it to deer hunt the previous fall. That would be the most common reason that anyone would be traveling cross country with a deer rifle in the spring.
The idea that he was traveling by motorcycle or car and that he left it at the turnpike oasis is a good probability. The amount and type of stuff that he was found with would have made walking and hitchhiking difficult.
I am thinking that it was more likely that he was traveling by motorcycle, based on his choice of clothing, and the fact that he had the rifle with him in the woods. Had he been driving a car, he could have left the rifle and ammo locked in the trunk. At the least, he could have left two of the three boxes there, rather than carrying them into the woods. He could have left the poetry books in a car as well, but carried all with him in a back pack. A motorcycle parked at a public oasis for any extended period of time could easily have been stolen by anyone with a pickup truck or trailer.
I am not sure what "presidential summer home" you may have seen reference to, but Dwight Eisenhower was President in 1958, and when he left the Presidency in January 1961, he drove to his home in Gettysburg, PA where he retired to and resided until his death in 1969. He may have owned his farm and used it as a "summer home" prior to his retirement, but I do not know for certain. Gettysburg is a good distance east of Bedford.