Your steps 2 & 6 cause problems for me... as soon as I remove the part from the chuck, it's a dead cert it won't go back in without runout and/or wobble. If I had a collet chuck, then I'd have no bother following your instructions, 'cos the arbor could be chucked in that once the shank was cut.
The way I made the part (or, would have done, had the bore cutting worked) was as follows:
1) Face & turn stock so it's running true & faced flat. Turn down to main arbor size (1.5", or maybe 1.25" for Mk2).
2) Centre drill, drill, ream a 3/4" deep hole to accept a suitable thread (I chose 1/2" BSW, as I have both taps & dies for that). Cut about 1/4" to clearance size, then tap the remaining material in the hole.
3) Turn a small portion of the end of the stock down to 1" to hold the saw. Once close, take fine cuts & test the fit often. Face the outer section to ensure it's flat.
4) Use the cut off-tool to make a couple of relief areas at top & bottom of shank. Turn shank down to size, then part off.
5) Turn down about 1/2" to the appropriate size for your thread. Cut threads as close to the shoulder as possible (I cheated: I cut them to 0.040" depth, then finished off with a die - this left quite a loose fit thread which I wasn't that happy with). Bore out some stock around the thread, to an outer (inner?) diameter of 1.003" or thereabouts. It should fit neatly over the saw, without too much slop. This is the bit that failed for me...
6) Once you're happy with the fit & finish, screw the two parts together & turn the outer diameter to whatever you're happy with (did that bit in Step 1!). Remove the first part, then part off the 2nd part from what's left of the stock. Job done!
If I can make Step 5 work, it never needs to come out of the chuck, which should guarantee next to no runout (less than 0.001"). I do need a left & a right handed turning tool (only got RH tools in the toolpost just now)