I had the pleasure several years ago of restoring a c. 1898 Model '97' Pigeon Gun with the full factory works done to it. The gun was in very good condition metal-wise and needed only some oil taken out of the stock head and then refinished to match the original.
As for engraving, I can vouch that there was no 'roll stamping' on any of it.....don't know about the others out there. The bolt has 'Pigeon Gun' engraved in a flowing script with a decorative border at its outer margins; it has an engraved pigeon immediately forward of the buttstock topside; ejection port side of frame has a hunter & dog with one dead quail on the ground & two dead in the air. Left side of frame has a very detailed scene of box pigeon shooting right down to the five trip lines. All hand-cut engraving and with very fancy XXX Winchester wood. It is a beautiful old piece and only wish it were mine.
This gun (not a knock-off or upgrade) has been with the same owner (a shooting friend) for over forty years now, who actually won it back in the early 60's on a coin toss. I guess we could conclude that they're a bit more esteemed today.
Rob H.