Hi John, welcome to the forum.
Wow, there's a question !!

But first, and in the unlikely event you've not already seen them, the PRs database includes the following;

Record_ID: 155602
Entry_Number:
Year: 1703
Month: Jan
Day: 17
Parents_Surname: COOPER
Child_Forenames: Thomas
Fathers_Forenames: William
Mothers_Forenames: Elizabeth
Mothers_Surname:
Residence:
Occupation: labourer
Officiating_Minister:
Event: Baptism
Memoranda:
Notes: old style date 1702/3
Register_Reference: GDR V1/34
Page_Number:
Parish_Chapel: English Bicknor
Soundex: C160

Record_ID: 155566
Entry_Number:
Year: 1700
Month: Apr
Day: 7
Parents_Surname: COOPER
Child_Forenames: Sarah
Fathers_Forenames: William
Mothers_Forenames: Elizabeth
Mothers_Surname:
Residence:
Occupation:
Officiating_Minister:
Event: Baptism
Memoranda:
Notes:
Register_Reference: GDR V1/34
Page_Number:
Parish_Chapel: English Bicknor
Soundex: C160

Record_ID: 155532
Entry_Number:
Year: 1698
Month: Feb
Day: 20
Parents_Surname: COOPER
Child_Forenames: Mary
Fathers_Forenames: William
Mothers_Forenames: not stated
Mothers_Surname:
Residence:
Occupation:
Officiating_Minister:
Event: Baptism
Memoranda:
Notes: old style date 1697/8
Register_Reference: GDR V1/34
Page_Number:
Parish_Chapel: English Bicknor
Soundex: C160

---

Possibly a previous generation of same family;

Record_ID: 155262
Entry_Number:
Year: 1677
Month: Feb
Day: 4
Parents_Surname: COOPER
Child_Forenames: Eastabell
Fathers_Forenames: William
Mothers_Forenames:
Mothers_Surname:
Residence:
Occupation:
Officiating_Minister:
Event: Baptism
Memoranda: BT Easabell dau Mr Cuper
Notes: old style date 1676/77
Register_Reference: P138 IN 1/2
Page_Number: 18
Parish_Chapel: English Bicknor
Soundex: C160

Record_ID: 110943
Entry_Number:
Year: 1698
Month: Aug
Day: 2
Surname: COOPER
Forenames: William
Residence:
Age_at_death:
Officiating_Minister:
Event: Burial
Cause_of_death:
Memoranda:
Notes:
Register_Reference: GDR V1/34
Page_No:
Parish_Chapel: English Bicknor
Soundex: C160

Record_ID: 110971
Entry_Number:
Year: 1700
Month: Sep
Day: 29
Surname: COOPER
Forenames: Elinor
Residence:
Age_at_death:
Officiating_Minister:
Event: Burial
Cause_of_death:
Memoranda: a poor widow
Notes:
Register_Reference: GDR V1/34
Page_No:
Parish_Chapel: English Bicknor
Soundex: C160

---------

This site's database contains 224 COOPER PRs for English Bicknor, the earliest is from 1581. These significantly predate the few across the Wye at Welsh Bicknor.
The earliest COOPER in English Bicknor records is

Record_ID: 154170
Entry_Number:
Year: 1581
Month: Jun
Day: 15
Parents_Surname: COOPER
Child_Forenames: Joan
Fathers_Forenames: John
Mothers_Forenames:
Mothers_Surname:
Residence:
Occupation:
Officiating_Minister:
Event: Baptism
Memoranda:
Notes: in Latin
Register_Reference: P138 IN 1/1
Page_Number: 18
Parish_Chapel: English Bicknor
Soundex: C160

The Church and village dates from Norman times, so I guess there were Coopers in the village then ?
http://www.englishbicknor.org.uk/thechurch.html

The most obvious route to Bicknor for new settlers was the River Wye, but from where ??... They may be totally unrelated to the Bicknor Coopers, but searching this site's whole database (of 3500 Coopers across the whole FoD) only gives a few older than Joan, and only by a few decades, and they're from north up the Wye then cross-country in Ledbury, or downriver and up the Severn to Westbury & Gloucester.However this whole site only contains 2 older COOPER PRs, and they are c1570 at Ledbury.

TIP: use the Advanced Search, when results are displayed, click the "Year" column heading to sort them chronologically http://forest-of-dean.net/joomla/index.php/advanced-search

HOWEVER the name was also spelt COWPER and CUPER - it's AngloSaxon derived from German word KUPER.
http://www.surnamedb.com/Surname/Cooper

Searching COWPER in our FoD PRs database, the earliest is again in Ledbury

Record_ID 215188
Entry_Number
Year 1582
Month Apr
Day 1
Parents_Surname COWPER
Child_Forenames Jone
Fathers_Forenames John
Mothers_Forenames Margery
Mothers_Surname WALKER
Residence
Occupation
Officiating_Minister
Event Baptism
Memoranda bastard daughter
Notes
Register_Reference BO92/1
Page_Number 116
Parish_Chapel Ledbury
Soundex C160

And the earliest CUPER also in that area,

Record_ID 423120
Entry_Number
Year 1604
Month Oct
Day 2
Parents_Surname CUPER
Child_Forenames Elizabeth
Fathers_Forenames not stated
Mothers_Forenames
Mothers_Surname
Residence
Occupation
Officiating_Minister
Event Baptism
Memoranda
Notes
Register_Reference P246 IN 1/1
Page_Number 20
Parish_Chapel Pauntley
Soundex C160

But next oldest CUPER are in Bicknor eg

Record_ID 155440
Entry_Number
Year 1691
Month Mar
Day 15
Parents_Surname CUPER
Child_Forenames William
Fathers_Forenames John
Mothers_Forenames Mary
Mothers_Surname
Residence
Occupation
Officiating_Minister
Event baptism
Memoranda Wm extended to William
Notes old style date 1690/1
Register_Reference GDR V1/34
Page_Number
Parish_Chapel English Bicknor

It seems that your English Bicknor ancestors are mentioned in the excellent British Victoria History site , but then again this could be said for most UK villages at that time. I have NO idea whether all men named Cooper at that time were cup/barrel-makers, or vice-versa;
"Trades supported by local woodland were represented in the early 17th century by carpenters, turners, a cooper, and makers of cardboard, platters, saddletrees, and trenchers."
http://www.british-history.ac.uk/vch/glos/vol5/pp101-117#h3-0005

Finally, as recently as 1881 Census the COOPER surname was common across the eastern half of the UK, so just including the FoD, and especially up the Severn in the West Midlands & Potteries.
http://gbnames.publicprofiler.org/Map.aspx?name=COOPER&year=1881&altyear=1998&a...

But COWPER was FAR less common across the UK, guess in the more populated area it's became known as COOPER ?, but like Cooper still fairly common up the Severn compared to the Forest.
http://gbnames.publicprofiler.org/Map.aspx?name=COWPER&year=1881&altyear=1998&a...

If you use the Soundex on the surname COOPER for English Bicknor

There is in 1690, an Elizabeth CUPPER - born to William & Elizabeth

a Mary CUPPER in 1691 to William & Elizabeth

and an Elizabeth CUPER in 1695 (father John)

and in 1677 Eastabell COOPER, father: William