Engine sputtering at about 65

Your timing can be 5 degrees late and it won't cause a sputter. Even 10*, and maybe more. I know because I have a dash-mounted, dial-back timing device with a working range of 15 degrees.If the timing is at least close,think about it; as long as the coil can light the fire at the sparkplug tip,
and you have already proven that it can by driving thru the problem;forget about ignition.
If it's related to throttle input, it's a mixture issue.IMO you have exactly 2 possibilities, the transition circuit, or the pumpshot.
The transition, in the case of a metering rod carb, is controlled by the step-up rods and more specifically the springs under them........which have to be synchronized to the manifold vacuum.
...And that leads to suspecting manifold vacuum, which leads straight back to the basics, testing the compression,the idle-vacuum,and maybe the valve springs, or lash.Then the fuel, the fuel level,the fuelpump output,finally the carb.You can keep on working on the carb, or jump in anywhere you like, but I doubt you'll get to the bottom of it in a reasonable period of time. I'm old, and I learned the value of basics many many years ago, about spring of 1968.

There's only one way IMO, that it could be timing related, and that would be if it was severely over advanced or severely late, both of which lead to vacuum issues, and thus step-up issues, and thus transition issues.
In any case
We're in your corner.

Wow that's a lot to absorb. So the new carb is installed, I made sure there were no vacuum leaks with the carb cleaner test. I set the idle set screws at 1.5 turns out and the idle speed to what I feel is a pretty solid resting idle. It's stronger through acceleration but still will wants to sputter up around 65, so the underlying cause is still here. I'm not upset about purchasing the carb since that secondary shaft was absolutely gone and I didn't want to mess with drilling and pressing new bushings in.

Will this eliminate fuel as the issue all the way from the carb to the start of the steel supply line that runs back to the gas tank, being that it's new fuel hose, new carb, fuel pump and filter?

If the timing can't be an issue, I'll look at the vacuum levels next. It used to be she idled at a perfect 20 psi but I haven't put the tester on it since the new carb is in place. I might actually buy enough vacuum line to run the gauge back into the car and drive it that way to see what it does when driving.