My interpretation from early on is the shafts both turn a little each way until the dogs hit the end of the slots. Does the revolve & change through each gear when all parts are seated in the left case. I reslise the main shsft is held over to the bearing in the right case when the clutch is fitted but I doubt that shaft play is very much when loosely fitted to turn the shafts. Could eyeball each gear set engaging & turning anyway. If I'm wrong just lift the mainshaft up flush with other shaft. By memory you had it all closed up & in the frame before finding this problem. Have you tried forcing it a little. Not just in gear? so it's turning the crank & all against compression. Detent ball bearing on the angle by the neutral switch holds neutral anyway providing the correct selectors are into the correct gears.

Ignore that I just looked back & answered my own questions. I guess can't be anything in the Kickstart if you haven't got that far except when you had it fully assembled, but is still doing it until cases are parted a little. Gotta be an answer 'there' as in why parting the cases fixes it.
 

I've marked up another photo showing the gears and which ones should "free wheel" unless the dogs are engaged.  

Blue are the "free wheel" gears.  

Red are the "locked" gears that are splined to the shafts. (First gear "locked" is marked as lime green and is actually machined into the clutch shaft)

All I can suggest is making sure the gears that are supposed to "free wheel" spin freely on the shaft unless dogs are engaged into that gear.  

If that passes, then assemble and try to see which dogs are engaging when it should be in neutral.  (I think you said it locked up when assembled in right case?  That indicates a possibility of two sets of dogs partially engaging at the same time.  By looking carefully, hopefully you can see the problem.

There really isn't anything "tricky" about these transmissions.  Changes were made over the years...  I'm not sure much was changed but make sure you aren't mixing up earlier CT parts with later CT parts just to be sure.  

Here is your picture assembled in right case where you said "does not turn".

The angle of the photo can distort things but this pic is good enough to make my point.  

The shift fork bushing (red line) is in the "2nd-3rd" groove in the shift drum.  When the drum rotates and the bushing moves up to the top of the groove the fork slides up and engages the dogs and you're in second gear.  Rotate the drum a little more and the bushing will drop to the bottom and you're in third gear.  



Because you should be in "neutral", that shift fork should be centered between the high and low positions in the drum groove.  It looks like the bushing is a little higher than halfway (could be an optical illusion) which means the dogs might be starting to engage second gear.  That's the kind of thing you need to look for. 

This link to another pic you posted looks like it's definitely going into second gear and is not in neutral.  imgur.com/a/51c3nZu

Last thing is wondering if you realize all the gears will always be engaged and spinning when one of the shafts is turning?  With no chain on the bike, friction might cause the sprocket to spin but there won't be any "drive" unless one set of dogs are engaged.   (More than one set of dogs engaged will lock the trans, big no-no but something has to be pretty far off, like an incorrect shift fork, for that to happen, very rare)

At this point a video that shows your exact concern is the next step.  It's possible what you think is a problem is actually "normal".  (Has happened to me MANY times, DOH!)