I recently did some work on a Powerstat, although smaller than the one you have. In my case, I split the windings of a 240 volt Powerstat to make an isolation transformer.
I see several problems with you project. From the photo, you have a three phase unit and using a different wire size will put the Powerstat out of sync with the other two. The reduced number of windings will also increase the current in the transformer and increase core heating. Finally, the construction technique used was to overlap windings on the inner diameter in order to have them lay flat where the wiper travels and maintain the winding density. Winding replacement wraps will require using a shuttle and it will be a challenge to obtain a tight winding with uniform wraps. You would also have a slight difference in winding height.
I see some possible approaches. I have in the past, stretched copper wire to straighten it, reducing the diameter in the process. It would take a 12% increase in length to reduce 18AWG diameter to .0381". It work if the insulation were able to stretch that much without failing. Another possible would be to wind with the 19AWG, living with the increased resistance of the 19AWG compared to 18.5AWG.
The 18.5AWG wire would have a cross section of 1452 circular mils and a resistance of 7.14 ohms/1,000ft, compared to 1288 and 8.05 for 19AWG and 1624 and 6.38 for 18AWG. You are probably dealing with in excess of 100 ft of wire.
You might want to check actual diameters of replacement wire. My experience is that nominal AWG sizes seldom have the nominal diameter and usually run smaller.
