With timing [which i'm sure isn't this issue] just mark the flywheel @ 3.2 then loosen points screw & let the points to touching & tighten screw, then they lift open at that point.
Not that easy because they move when tightening but practice makes perfect. Then you can refer to your mark next time.
Felt pen mark, white twink works good.
Forget all that though 'i think' & back to the carb.

Maybe really check the jets to make sure they are original Mikuni and not modified?  Needle and needle jet especially. 

Then I'd be swapping ignition. 

Sounds good, if I remember correctly I replaced the pilot with a genuine mik a couple years ago but have never touched the needle or jet so I will check that. Does the needle have markings on it? I've never noticed any. Been digging around for my rt3 coil once I find that I'll probably swap the ignitions. If that ends up working I might just leave the rt3 on the dt3 and VAPE my RT3. Thats a thing for another day though.

Yes, the slide needle should be marked and also have the Mikuni "square within a corner of a square" trademark symbol.  All calibrated Mikuni parts do, even the tiniest jet.

Check the needle jet carefully...  the long brass tube the jet setter threads into...  I had one that someone drilled out for some reason.  Ran super rich off idle.  hard to detect.

You said you had a spare DT3 carb as well?   That's how I figured out the original needle jet was drilled.  I had the same needle jet from another carb that visibly had a much smaller hole, verified by inserting shank of drill bits into it to verify inside diameter...  flashlight and magnifying glass also showed that the one had been drilled...  hard to see, but obvious at a close look and comparing to another one.  Kind of rare thing...  not easy to drill that brass tube.  But with the problems you're having, worth a look.

Aftermarket slide needles are fairly common and again can cause major issues.  Every aftermarket needle I've seen that runs bad runs rich. 

Yes does sound like an undersized needle or drilled jet tube 'as Mark says' which meters in the top guessing 5mm & can see the step looking up from the bottom end. With the needle down in the jet to try, it should have minimal clearance when in past the taper.
Also if it's wrong then want to be sure its not too short as it could come out of the jet on full throttle.
All unlikely stuff though. & i'll stick my neck out at risk of looking 'more' stupid & say problem is Nothing to do with ignition. Ign issues are erratic & this isn't. Might regret saying that. Have a happy day.

So tore the carb down, here are a couole
pictures. I did not however take a picture of ever little peice but every peice I took out of carb was genuine mikuni. 

I compared my spare needle jet to the one in there and they looked the same to me and not drilled out. The needle was able to fall all the way through the jet though. Needle: 5dp7 Needle Jet: 164 n8 

I decided to swap my needle jets as I thought it couldn’t hurt and when it fired up it revved freely, I thought I fixed it. But it soon went back to its 4000 rpm rev limit. Here’s some pics  Pictures

 

A 5DP7 needle has a max diameter at the top of 2.515 mm 

N-8 needle jet ID is 2.590 mm

That's a difference of 0.075 mm or a little less than 0.003"...  so needle will go through but should not have much clearance at all. 

I would say that is accurate of what I saw. It would fall through without any help but When holding it I couldn't see any light around the edges of the needle. Seems like a good fit.

Very easy to check whether the carb is your problem.

Take off the air cleaner boot, get a spray bottle with petrol in it.

Start and run the bike, and when you are at the throttle position, where it stops revving, squirt in some extra fuel, and see if that cures the problem.

Good to have a fire extinguisher handy if anything goes wrong. If it runs good with extra fuel provided, there is a very strong chance the carb is your problem.

If it is running rich adding more fuel would only make the problem worse.