I don't think I would be able to help since they decided to rewind the stock coils.

I can tell you from experience that, unless the coil is physically damaged, they don't go bad. There is never a reason to rewind an undamaged coil to make it work.
In this case (because of rewinding) the coils could be damaged beyond repair. You may need to buy another stator and start over. 

I have restored hundreds of stators and have never needed to rewind a coil...or even suspect  that it was wound wrong.
I have never needed to use an oscilloscope during a restoration.

If you would have sent in your stator for repair, you would have been riding a couple of weeks later.
This thread started in December and now it is about to be February... and you are still no closer to making spark.

I recommend you find another stator, leave it stock and start fresh. Or better yet, get another one, send it in, and when you get it back you will know that it will make spark and all the voltages.

I am pretty sure i have a complete original stator with flywheel i would sell if you don't want to mess with yours anymore. It looks to be in real good condition. Send me a message if interested.

I can see you're getting great satisfaction --albeit frustration as well--from sorting & rewinding yourself, so top marks. Well half marks lol & the rest when it running. It 'does sound' like rewinding the other way will sort it i hope.

I'm probably only holding up proceedings with my ideas but if all else fails it'd be nice to know if it sparks easily using a lighting coil wire fed back down the black from the top with source coil snipped off at the condenser.

HI,    Have not completely read your thread, but in reading the last post, I want to let you know  something I picked up  playing around with bikes.   On my 77/78 DT250,  I learned that  in the ole days,  it was possible for a bike to run in reverse as when the rotor turns,  it induces an voltage in the wire.   Turn the rotor the opposite direction, and the voltage is reversed, but the spark still happens.   This surprised a a few people when they let out the clutch and the bike went backward.

In my research,   I found out that a the ignition coil for a 77 and a 78 model had a different part number but the characteristics of the coil were fundamentally the same.   What I found out is  that a DIODE was added to block the spark in the reverse direction preventing the bike from running that way.

The coil from 1977 did not have a blocking diode in it.   

Perhaps you have an ignition coil that has a blocking diode in it.  

With a simple stator, when the rotor turns,  the polarity should be one direction and if you turn the rotor in the opposite direction, the polarity is reverse.

If  this is your case,   you can possibly find a coil without a blocking diode,  reverse the magnets (pole reversal),   or rewind the stator with the windings the other way.

However,  it seems to me the easiest approach would be to find another working stator.

good luck

Here is the graphic in the 78 service manual. If this is what is going on with your situation, then theoretically, if you swich the primary  ignition coil wires around, you will get spark in the other direction,
See the Note:

drive.google.com/file/d/1h9lvibQojHIsVyK.../view?usp=share_link

UPDATE- TODAY'S THE DAY GUYS! I got the damn thing to run! I decided to use my spare coil's core and I rewound it the right way (with maybe 30 extra turns for good measure, may be a bit rougher on the points but I wanted a nice hot spark) and what do you know the thing runs! Started it on some ether in the plug hole and wouldn't you know it the carb picked right up. Ran it for a good half hour just sitting on it soaking it all in before I shut it off (and then started it one more time just to hear it) and went inside.

Not quite done yet, though. I still have to re-integrate the stator wires into the wiring harness, seal up the flywheel case at the wire, actually mount the ignition coil, find where the ignition coil is actually supposed to wire into the harness, and put the battery back in (don't remember why I took it out, also don't remember how to put it back lol oops). Might also time the points right now that I can, as it sounds like MAYBE it's running a bit rough, but I'll let you be the judge.

I simply cannot overstate my gratitude to all of you who helped. I came to this forum with zero hope of fixing this bike and now with all of your help I get to experience the freedom of the open road. Not sure if all of you old heads remember what that's like, but to a 22 year old it means a whole lot. I might still post a couple more things about how to do the wiring but for the most part the case is cracked! Thanks for everything guys!

Also @DEET the only reason I went into this thinking the coil might be an issue is because the shop I took it to told me the coil was bad / out of spec, at that point I was in school and not working on it myself. I tried my hardest to find a good coil and it was nearly impossible (I had yet to learn of this forum) but I found a spare stator which included the coil in question so I bought it. I took it to the shop and he said the coil was even more chewed up than mine was (in fairness it was pretty badly damaged, marred visibly in multiple spots) and he didn't want to put it on. He then said he knew a guy who could rewind the original coil for $350 or so, and me being the arrogant ass I am I said get fucked absolutely not I'll do it myself. So I used calipers and determined the gauge of the wire, bought some on amazon for $20, measured and 3D printed some sheaves to stop the edges of the coil from spilling over, and then unwound and rewound it myself, counting the turns as I did (440). Upon re-winding I even double checked I was going the right direction before I started, but I realized upon making the second coil what my fatal mistake was. When you unwind the first coil, you spend about ten minutes spinning the wire in one given direction, let's say CW, before the thing is unwound. When I finished unwinding the second one, I realized my muscle memory told me to keep turning in the CW direction, which would have resulted in a backwards-wound coil. I think this is what I did with the first one - I wound it back up nice and pretty, checked the resistance spec, and gave it back. I guess I got what I deserved for winding it myself but truthfully I'm glad I did, I don't think you could make my stubborn self pay a man $350 to rewind a single goddamn coil if it had to go in my grandma's life support machine and you had a gun to my head. In any case, if I had been consulting you guys from the get-go none of this would really have been an issue I don't think.

Top marks at last & we'll be coming to you for advice very soon.

Friendly warning--just be a bit bit careful with ya #$%% language as it's part of the forum rules. Must admit i have to try hard at times to keep mine under control.

So now she's running & supposedly putting out 30 more winds of voltage--have a look in at the points in the dark shed when running & see how bright the arcing at the points 'is'. I guess you can't now compare with how it was in original form. If voltage is 'way too high', from my experience of using a lighting coil & voltage rising very high at revs, the arcing was 'wild' & caused misfiring & so went to the lowest output wire just experimenting. Anyway, congratulations & keep up the good work.

Congratulations! Well done.

When you're running it, make sure that the oil pump is working (and there's oil in the tank) or you're running a mixture of petrol and two stroke oil from the main tank - it would be awful if it seized after all your efforts in getting it to run. Sincere apologies if you knew this already.