I checked the ignition switch connection and one plug did push on somewhat when I checked that it was tight.
However, I was going to be thorough and also checked a number of other things as well last night. Of course I did all of them last night without driving it between them, so if it's fixed I won't know which one it was.
I pulled the carb cover off and found that there was some varnish-y looking crud on the bottom of the passenger side bowl. Cleaned it out well.
While I was at that, I checked the springs in the carb and saw that they were the heavy silver springs (8mmHg) where the carb instructions say that stock should be the orange 5mmHg, so I swapped those in. Rods/jets were stock. Figured that I'd get back to the initial settings and go from there.
On the Mallory, I pulled the top off and saw that the power wire to the coil had been somewhat crushed when I put the cap on last. It's just a solid wire, not stranded, and it was still very sturdy, but the insulation was pretty mashed. I straightened it out and put some liquid electrical tape over the mashed bit to prevent any possible arcing.
I also noticed that the screw for the cover in the corner that has the grounding tab for the coil had stripped out the screw hole, guess I overtightened it the last time I reassembled it. I was worried that this might affect the grounding of the coil, so I soldered a wire with an eye on it to the grounding tab and ran it back to the next cover hole to double up on the ground to the coil. I made sure not to overtighten it this time. I'll try to find a longer long screw for the one corner.
While I was in there, I pulled the cap and the Mallory ignition module to inspect them. Both looked fine, but the red power wire to the module was positioned where the module squeezed it against the vacuum advance rod quite hard. The insulation on the wire was dented in (not cut or broken though) quite well where the rod had worked back and forth across it. Seems like a design flaw to me on the module because there's no really clear/good way to route that wire. I tried to gently reorganize the red and brown wires that were working together to cause the problem and while the red is still touching the rod, it's definitely not stuck between the module and rod as badly.
Lastly, while inside the HEI, I noticed that the round rubber isolator/cushion in the cap under the coil was off center. It looked like it might have artificially compressed and pushed off-center the spring that goes from the rotor button to the bottom of the coil, so I straightened those. I also noticed that the area on the bottom of the coil where that spring contacts it looked to have some type of crud/coating on it, so I sanded it clean.
Called it a night after all of that. Went for a short-ish drive this morning before work and had no cutout/stumbling issues, but I'll have to drive it more to feel like it's really fixed.
I think the rod spring swap really helped, there's more power coming on faster when accelerating from part-throttle. I got to pass a Toyota Matrix who was doing 40 on a 50 MPH road. I won't say it was really "like she was standing still" but it sure as hell felt like it when driving a big honkin' Jeep from the 70's

Highest I'd pushed the revs to date. I really need a tach
I'll update this as I drive it more, more thoughts/suggestions are welcome!