Although I haven’t been an active Secret Searcher for very long, I fell down the rabbit hole hard and fast. Like many of you, I search online in my spare time from my armchair. I have a solution to propose but it comes with a caveat. NO ONE should dig in the site I am proposing but instead would suggest the community reach out to proper authority, leveraging the Media including EU and the Preiss family to attempt to find the casque.
The following solution is by no means perfect …
I’ll start with the Verse since each clue in Image 12 can be associated with the Solution:
In the Shadow of the Grey Giant, find the Arm that extends over the slender path ….
— The south/West tower of the Verrazano Narrows Bridge stands off the shore of Staten Island. It extends over the ‘Narrows’ waterway. Since the sun is south of the bridge, the tower’s shadow passes over the casque’s spot most days.
In Summer, you’ll often hear a whirring sound ….
— Boats engines make whirring sounds as they speed past the casque’s spot
Cars abound …
— There are thousands of cars passing overhead on the Verr Bridge close to the Casque’s spot
Although the sign nearby speaks of Indies Native …
— The key word here is ‘although’ because it references Hamilton but only as a misdirection. Fort Hamilton’s sign is on the other side of the Verr Bridge.
The Natives still speak of HIM of Hard Word …
— This is the important clue. As BP has demonstrated in Cleveland and Chicago solutions, he alters clues ever so slightly. In my research, the words HARD WORD were very frustrating until I realized, said with a NY Brooklyn accent, it sounds just like “Harvard”. My solution puts the casque in Fort Wadsworth in Staten Island. General Wadsworth is a graduate of Harvard.
in 3 VOLS …
— i have several theories for this line but nothing concrete
Take twice as many EAST steps as the hour or more. From the Middle of one branch of the V ….
— Every clue in the Image and Verse lead to this. If you go to Google Earth and check out Fort Wadsworth, there is a piece of the Fort called a ‘Battery’ and in this case, its ‘Battery Weed’. Battery Weed is shaped like a giant V and it even has a simple process to determine the middle of the V. If you count the ‘windows’ on the north side of the battery, there are 9. the middle is determined without any measurement simply by counting to the 5th window. Important clue: 22 EAST steps puts you near the end of the Battery, standing in the shadow of the Grey Giant, listening to whirring sounds and cars above you abounding. Walking EAST from the other 2 sides of the building do not make sense.
Look Down and see Simple Roots …
— As mentioned, the building is named Battery Weed. A weed is as simple a plant as simple can be.
In Rhapsodic Man’s Soil …
— this may be a wordplay on weed = Pot and when smoked you feel rhapsodic
Or Gaze North towards the Isle of B ….
— Bedloe Island is exactly North of the casque’s spot.
From Image 12:
The outline of the pic is the top half of the Verr Narr Tower
The ‘rectangle’ in Image 12 is the bottom half of the Bridge Tower (standing on the shore next to the bridge, it is a rectangle).
The Spires from the Image: is the lighthouse on top of Battery Weed
The panels with the red and blue ‘circles’ are the stones circling Battery Weed.
All the other clues in the image lead to Staten Island
Can’t stress enough that no one should dig on Federal property. If this solution is correct, when BP buried the casque in 1982, the area was not as restricted and it would have been easy to dig. But in 2019, not so much. I can guarantee, if you dig on Federal property, you WILL be arrested.
If this solution is correct, it should lead to addressing the search using legal, ethical methods to safely dig with proper authorization.
I have great admiration for Mr. Preiss and the adventure he has offered us all. I wish he were alive today so we could thank him for this amazing frustrating puzzle.
I want to give a shout out to Josh Gates and EU since his enthusiasm and willingness to spend time down the rabbit hole lead to weeks of my sleepless nights thinking about casques and shovels.

Somebody posted a near-identical solution a year ago:
viewtopic.php?f=32&t=7316&p=142985

Thought I had searched the old threads for all mention of Wadsworth but clearly I missed this thread. Thanks!

Good work on your part. Interesting thoughts. For my solve, Fort Wadsworth is the grey giant. So I believe the treasure grounds are in the “shadow” or “neighborhood” of Fort Wadsworth, meaning not too far away from the Fort.

Thanks but was a lot of wasted time since PaulM already figured it out. In reading the thread from July 2018, saw some great comments and suggestions. Was glad people took Paul’s observations seriously. Wish I had researched past solutions more thoroughly and saved myself from falling into the rabbit hole.
The one comment towards the end of the thread offered there was no exact spot to dig. From my research, the casque is buried at:
40 36’21.26 N
74 03’14.60 W
It is 22 east steps from the middle of the V.

ent66

Thanks but was a lot of wasted time since PaulM already figured it out. In reading the thread from July 2018, saw some great comments and suggestions. Was glad people took Paul’s observations seriously. Wish I had researched past solutions more thoroughly and saved myself from falling into the rabbit hole.
The one comment towards the end of the thread offered there was no exact spot to dig. From my research, the casque is buried at:
40 36’21.26 N
74 03’14.60 W
It is 22 east steps from the middle of the V.

I am not a local to the area so I do not know actually what it was like.
however I grew up on US Navy bases all over the United States. So I am really familiar with what Navy base security was like.
In 1982 your location was on Fort Wadsworth, Fort Wadsworth was turned over to the United States Navy in 1979, which used it as the headquarters of Naval Station New York. As a result of the Base Closure and Realignment Commission process, the Navy left and the property was transferred to the National Park Service as part of the Gateway National Recreation Area in 1995. So it didn’t actually have public access until 7 years after the casques were buried.
your theory is the casque was hidden on an active Navy base (not only Active, but the the headquarters of Naval Station New York.)
I’m just going to leap out here and say no- it wasn’t.

Unknown

Unknown:
The Natives still speak of HIM of Hard Word

There are several things whith have been pointed out in your solve as being unlikely…. and I agree.
However, if your solve were to be valid, a better explanation for this line would be the bridge itself. Since the name of the bridge was officially misspelled for so many years.