I have found NOS complete barrels on ebay but they come from the japanese market. Not always available but they do pop up from time to time. Some of the aftermarket springs dont come with a washer that inside diameter fits the barrel.
Seiko listed a barrell complete available for the 613 (206.613), but it has been unavailable since decades probably. Both 401.615 and 401.616 are listed compatible, and know to work well. https://www.thewatchsite.com/21-japanese-watch-discussion-forum/104345-seiko-6139b-mainspring.html
Attached the technical sheet.
The issue with getting a new original mainspring is now availability cost. For someone, $50 for something of dubious authenticity is objectable https://www.ebay.com/itm/401615-Main-Spring-For-Seiko-Movt-6105-6117-6118-6119-6138-6139-6309-6306-/303388168815
Another source could be the well know Adrian of VTA Australia https://www.vintagetimeaustralia.com
So it's normal that people looks for alternatives. Now, the height of 1.01mm (which seems strange as normally sizes are every .05mm) has been given by the OP from a website. But someone else measured (with calipers - ideally you want a micrometer) at 1.05: https://adventuresinamateurwatchfettling.com/2019/04/05/seiko-6139-6012/ and that is pretty much a GR2534X
Eventually he fitted a shorter MS, but he got a shorter power reserve. It could be that my initial suggestion of a GR24571X works well also, but I never tried either one.
Finally, when using a new MS no winder is needed, as its transferred straight from washer to barrel.