I started the thread Mule Deer referenced above. Based on our members' responses I went with the 3-groove in both of the Springfield 1903 rifles I sent Jesse, one to be a 338-06 and the other a 9.3x62.
I asked Jesse before sending them if he would leave off the new caliber markings so I could have a local engraver do a really nice barrel marking on my own dime. He said no problem, just include a note to that effect. So...I included a note with all the instructions for the rebores including an emphatic request to not mark the barrels. In addition, I wrapped each barrel with a piece of tape listing the caliber it was to become and the words NO STAMP. When the barrels arrived back to me, both pieces of tape with the NO STAMP label were still on the barrels where I put them but both barrels were stamped with the new caliber.
I have to say I am a happy customer, because they did nice work on the barrels and the caliber stamps don't look too bad at all, but if you are serious about getting your own custom marking on your barrel you might want to put a label that says something like, "hey, really really no kidding don't stamp the new caliber on the barrel!"
My sense is Jesse and Co. are really working as quickly and efficiently as they can to handle the volume they're getting these days with the fantastic turn-around times they are providing. So I get it that an unusual request might kind of fall through the cracks when they had up a head of steam.

Good luck with your rebore. I have an original Savage 99 in .358 and it is .595" at the muzzle, if that helps you any.

Cheers,
Rex