Mark,

Thanks for that explanation. One question. You mention 2 ball bearings. I am aware of the one that goes between the 2 clutch pushrods. I don't know about a second one nor can I find another on any of the parts diagrams. You mention it's
If either of those ball bearings are not the correct parts or not installed properly, one of the shafts could be shifted sideways which can engage dogs when they are not supposed to be engaged.  
Tsmitty

I'm speaking about the "assembled" ball bearings on the shafts that are complete with races and cages.  One near the clutch on the input shaft and one near the output sprocket on the output shaft. 

Sometimes one of those bearings have a special radius on the race edge and won't seat all the way without it, which will offset the shaft. 

Gotcha, thanks!

Me again

I'm wondering if it's possible that I did not get the right main shaft bearing, the bearing is flush against the keeper but, it is not flush with the case. It is flush on the opposite side where it was installed. Could that possibly be binding the trans when I put the right side case on? Eyeballing it, I would guess maybe 1/8th of an inch. I got these from Partzilla which I have had some parts issues, wrong part numbers which Mark has helped me with in the past.

Also, looking online for a trans (just in case) I noticed a washer on the countershaft. It's on the right in the picture. My transmission does not have one of these.

imgur.com/a/6CoNHoh
Ts

I don't see anything wrong with that bearing and it did look like the spacer was there on the sprocket side in earlier pictures.  Can you post pictures of your trans shafts out of the case?  

Have you been installing the sprocket and inner clutch hub parts and at least snugging down the nuts?  Pretty sure I said this before but clutch shaft must be pulled up against the ball bearing on the right and sprocket shaft must be pulled over to the ball bearing on the left.  The inner basket nut and the sprocket nut clamps them there.   

imgur.com/a/7KA1bhy

I had everything assembled and put the motor on the frame. I was attempting to install the chain when I first discovered the issue. So I guess yes is my answer would be yes Everything was snugged up.


Thanks again Mark.
Ts

I doubt my thought is relevant but if the pressed on small gear on the main shaft was pressed too far it'd lock up the larger gear next to it.

Quite relevant. What could cause that? Maybe over tightening? I had a tendency in the beginning.

Is there a fix since they are pressed on?

Side note: Mark that picture I sent with the thick spacer was the wrong trans. That was from a 1971. Sorry.

If the gear behind the small pressed gear is free to revolve then my comment isn't relevant.
If the trans was working before then nothing you've done would affect that running clearance.

Bottom R is my CT1
Bottom L is your CT3
Top is Sweger CT3

Posting this because I see a slight discrepancy in where the 2 gears meet each other. Two seem to be counter sunk, but your clutch side is raised almost appearing as if it were shimmed on other side of axle though I suspect not. I am not familiar w/nuances between 73 and 69 model engines, so this may be expected.