Timing
As the 1903 springfield book is back in view...
Springfield barrels had the thread milled in a fixture which had a master thread to allow timing.
The milling allowed both threading in a single pass and the cutting of a horrible square thread with stress concentrators at the corners (it was all done a long time before Griffiths and his calculations of stress concentrations inside tight corners). V form threads with nice radiused roots are far stronger. (Rope threads are the most resistant to fatigue - no sharp corners at all, which is why they get used in percussion rock drill rods - but I don't think you'd want to go there...)
I have a photo somewhere of a several foot length of coiled square wire that used to be the square thread in a drop hammer for standard penetration testing down boreholes. That one didn't hurt anyone when it stripped, but it happened in Angola
where skilled labour is ultra expensive and machine shops are very very few and very very far between, and spare parts have to wait for one of the 2 flights a week from Johannesburg (3 hour on a 747) and pay (extortion) import duty to a bunch of commies...
Number 4 Lee Enfields were made with the breech face of the barrel tight against an inner collar, and, the reinforce tight against the front of the receiver ring. They were meant to tighten to about 10 o'clock by hand, then crush to bring the sights upright. naturally that didn't always happen, so, in later production, peel off shims were used to get to the 10 o'clock position.
The little browning .22 semi auto rifle my mother used to have had a lock nut to take the wobble out of the interrupted thread barrel, when the sights were upright. As it was blowback, headspace was set by the bolt face resting on the back of the barrel, there was no problem with slight variation in barrel position.
Lindsay publications did a little reprint on the manufacture of Ross rifles. You might like to check that out, as the Ross (and the P14 / M17 Enfield and Lee Enfields) all had helical locking seats - effectively interrupted thread.
For your order of work, cutting the thread after the slot milling is going to produce fewer burrs and tears, and the ones you do make are going to be in an easier position to clean off. You can also bevel where the threads will come out into the slots, to minimise the chance of any little gouges there, and to ease the tool into the cut on the other side
If you thread first and then cut slots, you'll probably have a great weekend of work with a needle file, cleaning up the ends of the threads.
Keep us posted!