Here is the abc (copy and paste into Concertina.net to get a gif score and midi) of "Corn on the Cob" which is very similar to the "Loggerman's Breakdown" see HERE. I got this from a transcription by Vivian Williams who says this is "an awful lot like 'Logger's Breakdown'."

X:1
T:Corn on the Cob
C:Traditional
M:2/2
L:1/8
K:Bb
FE|D2FB dBFD|B2GB eBGE|A2Ac ecAc|BdcB AFEC|
D2DF dBFD|B2GB eBGE|A2Ac ecAc|BABc B2:|
|:A2|B2df b2bf|a2af gecA|B2df bfbf|afaf gecA|
B2df b2bf|a2af g2g=e|fbag f_edc|Bbfd B2:|

Now it's hard to hear the basic tune from McCutcheon's hammered dulcimer, but this (Corn on the Cob) looks like a good fit with what he plays. When you compare this (Corn on the Cob/Logger's Breakdown/Loggerman's Breakdown) with the unidentified tune, it doesn't really fit. The problem is, when you start listening to polkas, many of them begin to sound the same. So I really don't think there is any relation between the unidentified tune and the Loggerman's Breakdown.

Cheers, S. in Seattle