Hottigr's suggestion is a good one. I had my stock pump quit on me during a July solo trip from Chicago to Tampa a couple of years ago. It stopped working on me on the outskirts of Macom, GA on the interstate bypass loop. I managed to have enough momentum going to coast onto an off ramp and into a service station with a little boost from the starter with the car in gear.
The failure profile was a little different from what you are experiencing, but could well be a similar mechanical type of failure. Rather than stumbling, the motor would totally cut out, then the pump would start working again. Maybe yours is in an earlier failure mode stage than mine was.
I waited until evening when outside temps cooled down and was able to limp into my destination by running relative short periods and stopping for 30 minute cool down periods. I ran with the fuel pump cover door open to try and reduce whatever heat soak there was coming from the muffler. Even in the cool of the night, there was heat coming up through that door that I could not believe. I would not doubt that some of it was also engine compartment heat working its way back from the engine bay.
I installed a heat shield over the muffler when I put in the new pump. I also got my shield from Summit. I got the one that is really just a formed piece of aluminum held on by two stainless steel band clamps (like hose clamps). I remember reading that it is not good to wrap a muffler in any sort of insulating blanket. Supposedly, locking the heat in the muffler destroys the muffler pretty fast.
The point of the long story is that if it is your fuel pump, I would say it has already been compromised and should be replaced along with adding the heat shield. Getting stuck on the road, especially alone and the middle of nowhere, is no fun.
Gene