By My Understanding of the Story, The Camp would have been in the SE Corner of Huron Twp.
1876 Huron Twp would place it in or Near the Circle I Made
http://www.historicmapworks.com/Map...ille/Wayne+County+1876+with+Detroit/Michigan/
I Do not Live there

So unfortunately I May be off a Bit
But Perhaps a Member Here Knows the Location & Will Share Info ?
it looks to me Like Huron's Metro Park may have been the Area of the camp
as for exact location of the Cabin if Government History, holds True
it sat smack dab in the middle of the Nature Center out of Greed
the general rules for Metro Parks within Michigan
& The Parts that can be Interpreted to Deny Your Rights to Recreation
https://www.metroparks.com/about-us/rules-and-regulations/
so I Would advise against Asking the Park service, You will most Definitely get a NO .
You could ask a Grounds Keeper, being they are at the Lowest end of the Totem,
But would probably Remember if they Saw others there. in which case they may say yes.
but due to the Words Remove & Artifacts, I'd see about gaining permission outside the Border line.