Location(less?) in Glenorchy

THE CACHE IS NOT LOCATED AT THE LISTED CO-ORDINATES.  YOU NEED TO SOLVE THE PUZZLE.

I recently attempted to find a newly-published cache.  I looked at it on a map and thought "that's not right".  So then I searched lots of other parks, until the CO messaged me back and confirmed that it wasn't indeed where it was listed.  But that got me thinking - how can I make a locationless geocache without it actually being a locationless geocache?  Well, I guess a bit like this.

Your job is to find the co-ordinates.

The Puzzle

The cache is located at the co-ordinates: S 42° FG.H01'  E 147° XY.Z10'

To work out FG.H and XY.Z, you will need to combine some facts below, your own research (maybe ALL of the parks within the relevant range of the posted co-ordinates) and some (maybe lots of) trial and error:

• The cache is located in the Glenorchy City Council Local Government Area
• The cache is within 3km of the listed co-ordinates
• The cache is located in a park with a  metallic Glenorchy City Council sign out showing the name of the Park (e.g. not a car park)
• The park has a direct street frontage, has no toilet facilities and is not a sporting facility
• There are residences within 50m of the cache
• Neither FG.H and XY.Z contain the number 7 or 4
• H and Z are odd numbers that differ by not more than 4 
• FG multiplied by XY is an even number
• If you find rocks together with one of Time Magazine's most influential fake brands of all time, you are in the right place

Please include in your online log how many times you had a go at the checker.