A quick preliminary search on the web seems to indicate that "meadhan" has the meaning "middle", in Gaelic. This results from this bit of translation I found :

"ann am meadhan ar-a-mach nan Seumasach"
"in the middle of the Jacobite rebellion;"

(Of course, word order may be different in Gaelic, and "meadhan" might stand for "rebellion", but somehow I don't think it's likely... :moo )

"The Excellent Place of the Middle" ... ?

Now if we could find the Gaelic word for "earth", we'd be on our way to start translating Lord of the Rings !