Deltasaw1985, I too purchased an old Delta contractor saw with a 62-044 motor. The motor was shorting out and I found that it had a blown capacitor in the location you mentioned. I replaced it using the specs on the blown one, but it was a start capacitor. It worked for about 10 minutes of use and then blew the new one. Your post mentions that you found it was supposed to be a Run capacitor and you gave those specs.
I am thinking of buying the capacitor you mentioned in your post, but am curious how you determined which it was that you needed. I have googled and the only info I could find was this thread, so I hope you get this and will reply.
FYI, the capacitor I replaced (which I am now thinking may have been replaced incorrectly by the previous owner) was a Start capacitor "PTMJ43".
Incidentally, the saw seems to run without the capacitor with the wire ends taped independently to eliminate them shorting out, but I'm nervous that this is NOT a good solution, so am not using it until resolved. Any help from anyone that reads this would be greatly appreciated!