here's what I was able to dig up:
"8708 Old Kraftsman Arch-top Guitar – 1937
Similar to Recording King M-5
Body size 16 ¼” x 20 ¼” by 4 ½” deep
Curly maple back & sides, Carved spruce top
RW fingerboard with large “diamond” MOP inlays
RW adjustable bridge w/ MOP “diamond” inlays on sides
5-ply maple 14-fret neck
“Pointed dome” peghead shape with engraved MOP crown & RK logo with large diamond
“Checkered” or multi-ply binding top, single bound back, fingerboard & elevated pickguard
Hinged nickel tailpiece & individual Grover tuners"
source:
http://www.fox-guitars.com/Gibson-Made_Brands.html
I'm not saying that this is your guitar but it would appear to have some common features and it's the only mention I could find regarding the checkered binding. What bugs me is that the f holes are broken up similar to Kay's Sherwood Deluxe....
does your guitar have these dimensions?
are there any numbers inside at all? directly under the f holes?
can you get some better pix?
anyway, it sure is an odd one. time for antiques roadshow?
good luck