Hi Ryan. Sounds like a nice 'break in' trip. I'll offer a few thoughts. If you loosened some head bolts, (I had to also) you may want to re-torque them once you get the engine nice and warm. I learned this from Rocketeer.
Your head gasket may be okay, but you may be having a little coolant seep into the pistons once everything warms up and expands. This could have something to do with issue #2, but it might be something different.
I experienced a similar 'cutting out' when hard on the throttle during a long hill climb. My carb was starving for fuel. My filter was partially clogged. This may be your problem. If your gas tank has been sitting around empty for some time, it is not new, and the fuel lines weren't replaced, small bits of crud can break loose and block fuel delivery. It would be most noticeable when you are on the throttle.
Clearly, there may be other things to consider. You may just need a slight timing adjustment, or carb adjustment, but if you didn't change these, and the Willys performed well prior to your rebuild, I would look at fuel delivery issues.
I did just rebuild my Carter. Unfortunately, I don't have a good comparison to offer. I rebuilt the Carter so I could eliminate my Solex. For me, the Jeeps performance with the Carter is far better than with the Solex. I know this doesn't help you.
I am comfortable driving mine at about 40-42MPH. Any more than this and I feel like I'm mistreating the poor thing. I have taken it to above 50MPH a few times, but just for short down hill bursts.
Let us know what you find regarding #1 and #2.
Tim