In rebarreling a No.1, I would suggest looking at the various barrel blank makers on the home page of this forum as a starting point. Most offer contouring services to match your particular foreend if that is a requirement. Lots easier for the vendor to do the contouring, than your gunsmith, lots of time on the lathe which equates to $.
The No.1 is somewhat different than most bolt guns to rebarrel. The No.1 has its scope mounting on the barrel in factory form, which means that the gunsmith must clock the drill/tap for the quarterrib or whatever scope mounts. A bit ticklish to some, just a slight clocking error is pretty evident to the eye. The other clocking task is with the ejector slot in the barrel face. A bit more forgiving than the rib/scope mounting task, however is important not to go too deep because of case exposure issues.
The threading of the barrel to 16tpi on a 1" nominal shank is a common task in barreling. The gap between the breechblock and the barrel face can be reduced from the generous factory setting. Some think such helps accuracy, check with your gunsmith on his thoughts on this modification.
Ejectors can be had from Brownells or the factory for less than 10 bucks. A No.1 action is a No.1 action, the action proper for function only differs by the extractor type(head size).
No.1's can benefit from trigger updates, usually the factory trigger today is a bit much. Replacement triggers can be had or the orginal trigger can be reworked if necessary. Later models of the No.1's trigger removed the sear engagement feature of earlier models. A three screw trigger is available aftermarket as well as a set type trigger. To each his own there.
The forearm of the No.1 can be tuned for accuracy enhancements if necessary. A ton of information is on the net for such. Some No.1's shoot well from the start, some don't; but lots of information/opinions on the net to begin with. Your gunsmith will surely have his own opinions on the No.1 working well; just have to ask when the time is right.
The 220 No.1V is indeed a handsome rifle. I found that IMR4350 works pretty good in it, not overly fast, but seemed to have nice groups in mine.
I have done No.1's in 22lr, 17 centerfires, and 257 Roberts; kinda gotten away from the hard kickers in my later years. Not much to brag about really, just enjoyed the doing on my own.
Enjoy the No.1, hope it works out for you.