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"What can cause these kinds of engines to have a hard spot in the rotation? The starter seems to struggle in one area of rotation and I wonder if thats my root cause"
 
Is this "rough" spot even when the sparkplug is removed?
If yes, there could be a slightly bent piston rod, just a guess.

I would strip CVT (belt off) to get a clear pic where
the engine is "clutching", then try to start with CVT off, to find the culprit in that way.

THEN
starter motor out and revolve the motor by hand to see whether its really braking somewhere...

Are you trying to start with direct fuelling, without vac pump?
AND, do you have in your carbs idle-jet  this mini washer and o-ring?  (pls see pic)

CVT Came off and no real difference in hard spot.

Starter then came off, again no real difference in the hard spot.

I dont think it has anything to do with fueling, at all.

@tyguyc welcome here!
After all this read:
-100% sure the exactely same cylinder?
-piston rings reused and maybe not turned properly horizontally to avoid blowby (blue smoke)
-head gasket blowing (compression test?)
-once again check timing marks when at TDC
-sparkplug wet from fuel
-sparkplug out and check sparking
-check carb again

One more thing came in my mind:
 You said you replaced your carb.
 Your carb is fed by a vacuum fuelpump, where there are three hoses. (pls see pic)
One IN from fuel tank, one OUT to your carbs float chamber and one more, which is the vacuum TO/FROM carb, line. Maybe there is something wrong with tubes or this diaphragm is faulty.

Pls give a feedback for us to learn

Thank you Sir Ruffus. The fuel pump is out of the equation. I temporarily capped the vac ports and filled to bowl. (but it does work)

-100% sure the exactely same cylinder?
No but over %95.

-piston rings reused and maybe not turned properly horizontally to avoid blowby (blue smoke)
There is some blue smoke, but I believe that is the new head being in worse shape than my old head. But I realize it could be both.

-head gasket blowing (compression test?)
I did a DIY job to flatten the mating surfaces and the MLS Gasket was in decent shape. I didnt break out my compression tester but it is making good pressure.

-once again check timing marks when at TDC
Double checked and actually went one tooth advanced to try and get that intake valve to close sooner.

-sparkplug wet from fuel
checked and yes.

-sparkplug out and check sparking
checked good

-check carb again
I did plug in the old carb with the TPS Sensor and didn't make any actionable difference, but I also put 1-2 mL of gas down the intake and that didnt have any effect either.

What can cause these kinds of engines to have a hard spot in the rotation? The starter seems to struggle in one area of rotation and I wonder if thats my root cause.

Hello,
First time caller, long time listener.

I have a 2004. Got it a few years back non runner.
Had to disassemble the jug to find there was water that made it in there and pitted the walls pretty good.
Cleaned it out and slammed it back together and made it run.

But it was always really not fond of starting. It would seem as though there was a harder spot in the rotation. But it seemed like more of a backfire than actually caused by the rust.

Once it did start it ran pretty good. After 2 years of abuse like this the battery had been weakened enough to not really start this machine reliably.
When it was warm it started a little easier but still not really an easy feeling when you are XX.X miles from home.

So I ripped the top end apart late this winter to get it prepped for this spring. I had purchased  a 2008 head (the one with a decompression lobe?) and a slightly used cylinder earlier last year. And just purchased a piston and base gasket this year, dont judge my sloppy rebuild skills.
The piston ended up being a smart purchase bc mine was pretty scored on the bottom sides. reused the rings and headgasket.

Then yesterday I put it all together making sure that the T mark on the flywheel lined up with the 2 dots on the cam (and used the screwdriver method to make sure that the piston was at the top of the stroke)
torqued it all together, put the valve cover back on and threaded the spark plug in.

It rotates better now but still seams like there may still be a spot where its a little tighter than the other spot in the rotation.

And it still does not like to start easily.

It still backfires a little like the timing is too advanced. It did cough a few times when I tried to start it and choking it did seam to help a little. But not enough to get it to run for more than a second, if that.

Also this is with a new Carburetor but it never ran with the carb off it (just as a test).

So 3 questions.
What is wrong with my poor scoot? I would love to ride it but its so hard to start I hardly break it out.
What is the proper way to make sure that the ignition timing it actually proper?
AND
What is the the default setting the CDI Uses when its not getting the TPS Signal?

I'm Sorry and Thanks, in advanced.