I don't know whether this information will just muddy the waters or maybe provide a clue for proving William Hooper from Churcham.

Taken from the list of landowners for the Parish of Churcham at time of Enclosure in 1802 there was only one Hooper mentioned.
He was Jeremiah Hooper who was Copyholder for several plots of land.
From the 1839 list of landowners for Bulley, there also was only one. Also named Jeremiah Hooper.
If you want to know the exact location of these plots, let me know. I wouldn't be surprised if the boundaries from then still match fields today.

Sid Toomey

Piece: Q/SO/12 (part)

Deputation to William HOOPER to act as gamekeeper for Hartpury by Robert Carring, Eq. lord of the manor, made 5 February 1816, registered at Quarter Sessions 16 February 1816.

+ a much earlier Jememiah HOOPER also a Gamekeeper

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Appears to be a connection between the Churcham and Hartpury HOOPER's through occupation.

I think that should read Robert CANNING at Hartpury House. They were related by marriage to the Crawshay iron-masters of FoD renown. The Canning family built the current House in 1813 and their descendants lived there until after the Great War, when they were so disillusioned by the changes to English social-life & structure that they broke up the Estate and sold the farms to the tenants. In 1948 the House became an agricultural college, and is now a sports college including an important Equine Centre producing Olympic gold medal winning showjumpers.

I only found this out very recently, while researching a friend's tree; to my surprise the only one of his ancestors who moved away from their Lincs & Notts farming homeland was a G-G-Uncle who was Gamekeeper at Hartpury House in the 1911 Census, and remained in north Glos for the rest of his life. My friend was delighted as he is also a countryman still in deepest Lincs who actively enjoys field sports and country pursuits.

More info abt Hartpury House and the Canning family here;

http://www.hartpuryheritage.org.uk/village-history/manor-of-hartpury/

https://www.heritageopendays.org.uk/visiting/event/historic-hartpury-hartpury-house

http://www.forest-of-dean.net/fodmembers/index.php?mode=thread&id=40608

http://www.hartpury.ac.uk/about-us/history/

The Lodge where the Gamekeeper lived in 1911 is marked on this 1883 O.S. map. The House is midway up the lefthand edge of the map, the Lodge is east of it near Moor End.
http://maps.nls.uk/view/101453142

The local pub the Canning Arms was named after the family, it only closed-down relatively recently.
https://forest-of-dean.net/fodmembers/index.php?mode=thread&id=29837

Forest of Dean records

Marriage at Churcham - 4 December 1786

Thomas HOOPER
residence: Bulley
Mary ROWLES
residence: Bulley
Licence
Both sign
witness 1: Thomas DOWLE and mark of Ann DOWLE other witness: William ROWLES

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?

There doesn't appear to be a transcription of this Licence in the Forest of Dean records.

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Perhaps other Wills may list the children of Thomas & Mary HOOPER

e.g.

Jeremiah HOOPER - Bulley - 6 June 1807
Edward HOOPER - Bulley - 7 July 1821

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Looking at the Gloucesterhire Records Office Catalogue on line - the HOOPER's appear to be Gamekeepers - and could be working in other areas, as did my family - and some of their children I have been unable to find their baptisms.

Piece: Q/SO/9 (part)

Deputation to Thos. HOOPER to act as gamekeeper for Churcham by The Dean and Chapter of the Cathedral Church of Gloucester, lord of the manor, made 20 October 1777, registered at Quarter Sessions 22 October 1777

Piece: Q/SO/12 (part)

Deputation to William HOOPER to act as gamekeeper for Hartpury by Robert Carring, Eq. lord of the manor, made 5 February 1816, registered at Quarter Sessions 16 February 1816.

+ a much earlier Jememiah HOOPER also a Gamekeeper

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Appears to be a connection between the Churcham and Hartpury HOOPER's through occupation.

William HOOPER - 54 - Superannuated Greenwich List Seaman - born Gloucester
Sarah HOOPER - 56 - born Weymouth
Emma HOOPER - 16 - born Weymouth

??? needs some work

Family Search

Christening 1835, Melcombe-Regis, Dorset

Emma Mary HOOPER - parents William & Sarah

1841 Census Wyke Regis, Dorset
Queens Row M & P B

Will BENNETT - 60-64 born Dorset
John BENNETT - 20-24- born Dorset
Sarah HOOPER - 40-44 born Dorset
Edwd HOOPER - 13 (?christened 10 May 1829, East Stonehouse Devon, parent: William & Sarah)
George HOOPER - 11
Emma HOOPER - 6 - born Dorset

Jeremiah HOOPER - 30-34
Hannah HOOPER - 30-44
Edward HOOPER -40-44

-

Jeremiah HOOPER christened at Churcham - 4 July 1787 - parents: Thomas & Mary

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Witnesses: Edward HOOPER marked + Esther FRANKS

Had a very quick look and at Arlingham: Jonathan & Esther FRANKIS has at least two children christened at Arlingham - 9 April
1820 named Anna & Emma (need to look for others).

On the Forest of Dean records marriage at Awre - 15 March 1808 (the Licence on this website is dated two years before!)

Jonathan FRANKIS of Painswick married Esther HOOPER Spinster - by Licence

Notes: BTs show Bride as of this Parish

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29 April 1806

Jonathan FRANKES aged 21, Bachelor, Farmer of Painswick
Hester HOOPER aged 21, Spinster, residence: Upton St Leonards

marriage by Licence, he signs

Memoranda: sworn before Thos RUDGE to marry at Painswick

Therefore: Esther HOOPER needs more research.
!!

Esther FRANKIS buried at Arlingham - 23 July 1823 aged 34 c1789

Esther HOOPER christened 5 January 1789 at Churcham, parents: Thomas & Mary

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1841 census Painswick

FRANKIS

Jonathan - 56-60
Mary - 29-33
Emma - 21-25
Ellen - 1

0000

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Both Thomas HOOPER aged 69 is buried at Arlingham 11 May 1822 and his wife Mary HOOPER died 17 November 1821 at Arlingham