It’s easier to offset inward, if you rebuild the ring a little. i’ve done a very quick example - the surfaces aren’t great but it’s quick. (I say easier - I mean it was easier to offset inwards in this instance with the shape you’re looking for - if you already have the outer shape you want. If you want to offset outward you’ll have to do a little more rebuilding and messing around)
I basically duplicated the borders of your surfaces and swept with 2 rails to remake the ring without the split in the middle (at the bottom)
It was done as a single surface then I duplicated the border on the top face and copied, scaled and then lofted.
It might be a good idea if you redraw the basic geometry with circles and lines tangent then try extruding and lofting again.
octagonal_signet-2DC.3dm (686.2 KB)