Re iterating what has already been posted, when makingb the internal mthread in the adaptor, mto screw onto the 62 x 1.25 mm flywheel, the bore should be 60.75 mm, but should be very slightly truncated to avoid root/peak interference, so the 60.83 mm for 70% engagement will be the dimension to which I would attempt to work. It will be worth making an undercut at the end of the thread into which the tool can run.
The external thread onto which the extractor will be screwed should be 60 mm x 1 mm pitch, again, very slightly truncated. Kempe’s Engineers Year book says that the thread should be truncated by H/8, where H= 0.86603 p, so for a 1 mm pitch by 0.1083 mm, to 61.783 mm diameter.
If it needs to be said, start with a light cut, and gradually reduce the depth of cut as the thread progresses.
If you are new to screwcutting, (I am NOT expert!) My preferred method would be to withdraw the tool after every pass, and reverse, without disengaging the half nuts. That should remove backlash problems with the leadscrew, but ensure that you take out the backlash when readvancing the tool for the next cut.
It will take some torque to cutb then thgerad, so a Mandrel Handle will be needed. Unless back gear can be engaged, the lathe may lack nthe power, wnyway, and with such large diameters, the rotational speed needs to be low; another reason for driving the spindle by hand..
As Hopper says, lubricate the forcing screw well, (It should be large diameter, but of fine pitch, 1mm?) to maximise forces. It might be worth centre drilling the end and inserting a ball bearing, (3 – 5 mm diameter?) to minimise friction. Once fully tight, as he says, a tap on the end with a mallet is likely to jolt the flywheel free.
If that doesn’t work, try applying heat from a heat gun to the outer edge of the flywheel. As the heat soaks through to the middle, the flywheel should loosen its grip on the cold shaft.
It might jump some distance once it loses its grip! And will be quite hot.
Howard