Welcome, John.
As I said on NGDF, I haven't seen a badge like that before but I seen no reason to think it's not what it purports to be, especially if you acquired it in Farmington.
Do you have a picture of the whistle? I'm really curious to see what it looks like, and I wonder what Bob Werner's reason was for thinking it might have been from SR&RL No. 15 in particular if it's not marked.
Both pieces are very rare and deserve a good "forever" home, and I hope that you would consider donating them to the WW&F Railway Museum archive (which includes artifacts from all the Maine Two-Footers and not just the W&Q/WW&F).
-Philip Marshall