That is a larger thread than I was picturing, it must be a big grinder.
You have a learning curve ahead, not really steep but it might prove frustrating at times. Presumably you have turned the replacement shaft so you want to be sure of success before attacking it.
What material did you use? Medium carbon steel something like 1045? Getting a smooth finish on 1045 or 1018 on a manual lathe running slowly can be a real bear; these materials will tend to tear when cut slowly which is the case with threading. I suggest turning some replicates of the thread stub on the shaft and practising.
Grind your own tools out of HSS and put on a top rake of maybe 5 degrees; I am of two minds whether to suggest you do the two flank approach so I will describe it with the caveat that maybe this is getting more complicated than necessary.
As I mentioned for doing the flanks separately you first cut a vee thread that fits within the acme profile and of course you don't worry too much about the finish on this. Then you grind 'half tools' for the acme and you make the top rake perpendicular to the flank; this is different to a full profile tool which by necessity has the rake perpendicular to the axis of the thread.
When doing the two flank approach you set the compound parallel to the axis of the thread and use the cross slide for the infeed. With only one flank being cut using the compound for infeed at the half angle is not needed but what is needed is a way of tweaking the half tools sideways so you can center them on the previously cut vee thread.
You will likely need to experiment with cutting fluids. The two big problems when running slow are the build up of material right at the cutting edge and the failure of the chips to form a nice curl. In your practice runs experiment with things like tapping fluids, the high sulfur threading lubricant used for cutting pipes threads in a threading machine (I think The Home Depot has it), weird things such as lard or even gear oil. Come to think of it lard may be historically appropriate for remaking an antique.
With luck an perseverance you will finally get the conditions to cut a thread with flanks that almost look ground. When grinding your toolbit use a trick I was taught about half a century ago; grind on the side of the wheel so the grainding action is parallel to the cutting edge. This avoids creating minuscule grooves in the cutting edge which happens with conventional grinding from the grit. It does require a bit of practise to hold it correctly and safely against the wheel especially for the top rake and you have to be sure nobody from OSHA is watching because side grinding is frowned upon.
Good luck. Or should I take the attitude that luck has nothing to do with it because it is dedication and practise that is needed?
EDIT: after uploading my post I see Clive603 suggesting a similar approach. I prefer to use a vee tool for the 'pre-thread' simply because chip clearance and leading edge clearance can be problematic with a square tool but either approach can work. Similarly the single acme tool for finishing works and the only possible benefit from my approach is a better orientation of the top rake; also you don't need to grind the 29 degree include angle because you can tweak the toolbit to get the cutting edge correctly aligned.