Extraordinary is www.newtownabbey.gov.uk/leisure/downloads/CarnmoneyHilll.pdf which has an introductory page, topsy turvy , yes upside down text and pictures. I have never seen this on any website before.
"Toppy toosy" certainly sounds like a local colloquialism.
Perhaps a manifestation of that well-known Ulster custom,
endemic in the area:
"Having a little tease with The English!"
(as she is spoken ...)
Possible original candidates might have been:
1) Top (of the) Toun;
2) Two Tops (or Taps).
There is also a "letter agent" named TOPLEY in one of the Belfast directories.
Maybe it was his "Shank's pony" short cut over the hill?
The track that TOPLEY's tootsies trod!
There's a Tappatourzee/Tappuetousie (local pronunciation Tap a toosy) in Knockaduff townland, Co. Londonderry.
The name according to Jameson's Scottish Dictionary means 'dishevelled head.'