First and foremost, the value in this axe is that it was your grandfathers. It looks well used and cared for. Don't ever let it go!
As far as the Rixford-ness, it sounds like you already know that they produced high quality axes. The mystery is in 'closed in 1956 and stamped R57'. There are 2 ways I would approach this; questioning when they closed and questioning the stamp as the year.
Both ways are related, actually. The first would be recognizing that the 'closed in 1956' is mostly a reiteration and restatement of Tom Lamond's research. Tom was a pioneer in researching axe history and I doubt there will ever be his equal (given the resources available to him, e.g. no real internet, it is incomprehensible how much information he gathered, recorded and shared (for free in a lot of cases)). As time has gone on there are certainly things that he had declared that have been updated based on new information being surfaced. I've spent some time in the Rixford company archives (housed at UVM) and haven't discovered any documentation disputing his claim. Also no documentation affirming his claim, so there you have it.
Now to the 'R' stamp. Is the number the year? Tom refers to this as a catalog number. This is super-wise and super-insightful of Tom (and safe as a researcher). There is a clear relationship between the number stamped and the age of the axe (a limb I'm willing to put my kids on). And it appears to gradate annually. I also know that Rixford put out price lists for the next year in Oct of the prior year (I have examples from the 30's and 40's). So, I have always treated the 'R##' stamp as we would treat a car model. The 2022 car model's are already out but it is still 2021. That is where Tom's language of 'catalog number' comes in as brilliance. I think he was spot-on!
All my conjecturing aside (happy Halloween!), treasure that axe! All 4 of my grandparents passed before I was born and I've never come close to anything they owned. If you treat it like your grandfather did, it will outlast you, your children, your children's children...
Regarding the double-bit-ness, they probably just produced fewer double bits because, well, chainsaws rendered axes for felling trees largely dead at that point and changed to focusing in on camping. So there probably were fewer DBs produced, but just because of the marketability of the tool in the mid 50's (we would see MET take advantage of the foresight of Snow and Nealley making the hudson bay axes by birthing the Norlund line within the same decade).
