First of all, you need to get the LATEST ESS driver from Warp9. Anything before that does not work properly.
Second, trying to use info from the HAAS machines is not a good idea. HAAS do some things a bit differently. You need to read (study) the Mach3 doco and experiment a bit.
I found the Mach3 G76 code to be overly complex, as it tries to do everything. Well, fine, but . . .
I simplified it, cutting out tapered threads and a few other bits one never uses. I find it does the standard threads quite well.
For the record, I routinely use Mach3 for threading. Granted, sometimes I cut the thread not quite all the way and finish off with a tap or die, but there is a good reason for this. With a standard 60 degree V-tool you will get a 'thread', but it will not have a profile which complies with the Standards. You can use a matched threading insert - matched to the single size of thread you are cutting, but that works out expensive. A commercial tap or die does make the right final profile.
Cheers
Roger