I believe on a factory resharpening the whole reamer is reground... it's the same dimensions as a new reamer... this could be done over and over moving 'back' on the reamer slightly each time until you run out of sufficient reamer...
That matches what I have been told.
Stoning the flats is a fair enough way to extend the life of a reamer, but it won't do what needs done as far as restoring it to new condition, as it will reduce the diameter, if only slightly (maybe tolerable) however it will not deal with and wear on the actual cutting edge, so you could well enough stone the front face to near perfection, but not get the worn sections off the actual cutting edge.
For those interested in such, there is a drawing and some discussions of a reamer stoning jig in Guy Lautard's The Machinist's Bedside Reader series of books. He admits to botching up the drawings, as he reversed them, but if you are at all capable of building a jig like it and using it, it should cause you no troubles.
It boils down to a risk vs. reward assessment, which each guy will have to work out in their own terms. A regrind, plus a wait, or simply pay the toll and buy a new reamer. With a 100 jobs behind it, maybe both a new reamer and a regrind, and then you can directly compare. And, one could be in use with the other as backup, and you'd not be out while the dull one gets a trip to be renovated.
I ran a Tool And Cutter Grinder in the shop I last worked at. Did mostly drills and chucking reamers, either just a sharpening, or making custom sizes and stepped hole reamers. While the manual T&C grider could have been set up to grind a chamber reamer, or regrind one, the time and headaches looked like they were not near worth the effort compared to just buying one. For what it takes to make one, they are cheap!