To be a real pedantic ass (and further derail the conversation) I'm entirely sure that this bit you've quoted does mean within 500m of a Great Walk track. If it meant any track there should be an Oxford comma; "Within 500 m of a Great Walk Hut, or track". Also tracks in general are covered by the bullet point immediately above this ("vicinity of.. tracks"), so it's reasonable to interpret this as a specification for Great Walk tracks.
That said, use some good common sense, and maybe worth a few people contacting DoC to get it reworded so it's less ambiguous.
To come back to @SAUM's question, check out where there are less-used tracks/routes in the Mt Oxford/Thomas/Grey region, just be aware they can be very busy with trampers.
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