Good morning hacdlux,
I have had this issue for a few years now. I have run many parts where the threaded OD was the OD of the bar. One was threaded the entire 16" length of the part! (They wouldn't accept all-thread for one reason or another!) Sometimes it's not bad, sometimes you can pull all of your hair out. The material you are cutting is the biggest factor. Something like mild steel or easy alloys, (4140), are easier to take care of the chips than stainless, just like in normal turning. 316 stainless is a booger, for sure.
Some things I found that helps, but doesn't always solve the problem:
The biggest help was using an insert with multiple points on it. I think Iscar calls theirs "twin-thread" but other manufacturers have similar style inserts. They seem to help with chip control and it takes half the number of passes of a standard insert. The only drawback to them is that they are typically only available for course thread pitches of 20 TPI or less. Being long running or returning work, it may warrant spending the extra money to order specials for the finer thread pitches. Again, this helps, but is not a cure-all.
I tried the HP coolant in our Tsugami B0326 on the 16" long part previously mentioned and that only made a slight improvement, if any. Granted, this part was 316 stainless. You can experiment with different nozzle directions to help get the best benefit from it, but it might take a while.
If the twin thread inserts are not available for your needs, try any and all inserts from different manufacturers with different chip breakers. This will definitely take a while, but if you find the right insert, it can virtually solve your problem.
For threads with a length of engagement as short as yours, I would possibly try running them in one of our E-, or M-series Citizens, as they are a 3-path control. Then you can just tell path 1 to stick the material out there and path 2 can thread it. This works wonders if you have a 3 path machine.
You can also try the dog-leg on the threading tool. For the size of the parts you are talking about, rigidity should not be a problem with the holder. I would be more worried about the bar you are threading. But even then, you are only talking about 2 times diameter, so that shouldn't pose a problem.
Also, being in the Tsugami SS26, your holders are horizontal like those in our B0326. Try experimenting with orientation of the holder. Try it on the back gang where the holder is upside down. This way gravity can help pull the chip down, away from the bar you are threading.
There are many ways to skin a cat. If you have the patience, and have the time and materials to be persistent enough to try, you will get it figured out. Good luck and have fun!
Mike