Apart from John Hogg Smith which I've already listed the details for...trawling through all the men named John Smith, the following are on the nominal roll with non-NZ NOK, or NOK that are not close family (so they could be from anywhere).
Surname SMITH
Given Name John
Category Nominal Roll Vol. 1
Regimental Number 6/3162
Rank Private
Body or Draft Seventh
Unit or Regiment Canterbury Infantry Batln
Marital Status S
Last NZ Address C/- D Hampton Culverden
Next of Kin Title G
Next of Kin Surname SMITH
Next of Kin Relationship Father
Next of Kin Address Seggieden Kennethmont Aberdeenshire Scotland
Surname SMITH
Given Name John
Category Nominal Roll Vol. 1
Regimental Number 13/738
Rank Trooper
Body or Draft Second
Unit or Regiment Auckland Mounted Rifles
Marital Status S
Last NZ Address Greens House Whakatane
Next of Kin Title T
Next of Kin Surname SMITH
Next of Kin Relationship Brother
Next of Kin Address 1 Market Hill High St Sheddall England
Surname SMITH
Given Name John
Category Nominal Roll Vol. 2
Regimental Number 8/4222
Rank Private
Next of Kin Title John
Next of Kin Surname IRONSIDE
Next of Kin Relationship Brother-in-law
Next of Kin Address Pembroke Otago
Roll 28
Page 15
Occupation Coach-Driver
Surname SMITH
Given Name John
Category Nominal Roll Vol. 3
Regimental Number 37558
Rank Lance Corpl
Next of Kin Title William
Next of Kin Surname SMITH
Next of Kin Relationship Father
Next of Kin Address Baillieston via Glasgow Scotland
Roll 55
Page 39
Occupation Miner
Surname SMITH
Given Name John Bremner
Category Nominal Roll Vol. 1
Regimental Number 11/429
Rank Trooper
Body or Draft Main Body
Unit or Regiment Wellington Mounted Rifles
Marital Status S
Last NZ Address Kaponga Taranaki
Next of Kin Title Robert
Next of Kin Surname SMITH
Next of Kin Relationship Father
Next of Kin Address 34 Park Drive South White Inch Glasgow Scotland
Surname SMITH
Given Name John Edward
Category Nominal Roll Vol. 3
Regimental Number 62161
Rank Private
Next of Kin Title James
Next of Kin Surname OLD
Next of Kin Relationship Friend
Next of Kin Address Te Kuiti
Roll 75
Page 15
Occupation Farmer
Surname SMITH
Given Name John Hardy
Category Nominal Rolls Vol 4
Regimental Number 71413
Rank Private
Next of Kin Title Mrs J J
Next of Kin Surname SMITH
Next of Kin Relationship Mother
Next of Kin Address Welby Grantham Lincolnshire England
Roll 81
Page 11
Occupation Driver
Surname SMITH
Given Name John James
Category Nominal Roll Vol. 1
Regimental Number 6/354
Rank Private
Body or Draft Main Body
Unit or Regiment Canterbury Infantry Batln
Marital Status S
Last NZ Address C/- C White Flaxmere Blenheim
Next of Kin Title John
Next of Kin Surname SMITH
Next of Kin Address 31 Strathleven Rd Brixton London England
Surname SMITH
Given Name John James Walter Mason
Category Nominal Roll Vol. 3
Regimental Number 57321
Rank Private
Next of Kin Title E
Next of Kin Surname YOUNG
Next of Kin Relationship Friend
Next of Kin Address Ward Street Ellerslie Auckland
Roll 70
Page 21
Occupation Driver
Surname SMITH
Given Name John Leslie
Category Nominal Rolls Vol 4
Regimental Number 75284
Rank Staff Sergt
Next of Kin Title Mrs F J
Next of Kin Surname SMITH
Next of Kin Relationship Mother
Next of Kin Address The Grange Crookwell New South Wales Australia
Roll 88
Page 16
Occupation Salesman
Surname SMITH
Given Name John Michael
Category Nominal Roll Vol. 2
Regimental Number 35487
Rank Rifleman
Next of Kin Title D
Next of Kin Surname MCDAIRMID
Next of Kin Relationship Brother-in-law
Next of Kin Address Waitati Otago
Roll 47
Page 13
Occupation Labourer
Surname SMITH
Given Name John Pickering
Category Nominal Rolls Vol 4
Regimental Number 71908
Rank Private
Next of Kin Title Mrs K N
Next of Kin Surname ROBERTSON
Next of Kin Relationship Friend
Next of Kin Address Main Road Lower Hutt
Roll 81
Page 19
Occupation Engine-fitter
Surname SMITH
Given Name John Richard
Category Nominal Roll Vol. 1
Regimental Number 12/2120
Rank Corporal
Body or Draft Fourth
Unit or Regiment Auckland Infantry Batln
Marital Status S
Last NZ Address 48 Ponsonby Rd Auckland
Next of Kin Title J W
Next of Kin Surname SMITH
Next of Kin Relationship Father
Next of Kin Address Willow Lane Norwich England
Surname SMITH
Given Name John Sydney
Category Nominal Roll Vol. 1
Regimental Number 10/691
Rank Private
Body or Draft Main Body
Unit or Regiment Wellington Infantry Batln
Marital Status S
Last NZ Address Matemateaonga Eltham
Next of Kin Title J S
Next of Kin Surname SMITH
Next of Kin Address Ruthlyn Wellington Shropshire England
These John Smiths were killed in the war:
Gunner John Black Smith 2/2543, DOW 6 October 1916. NZ NOK
Private John Brown Smith 12/251, KIA 23 April 1917. NZ NOK.
Lance Corporal John Charles Smith 13644, KIA 13 September 1918. NZ NOK.
Private John Ernest Smith 10/1340, KIA 16 May 1915. NZ NOK.
Rifleman John Hardy Smith 71413, DOW 10 October 1918. NOK Mrs J.J. Smith (mother), Welby, Grantham, Lincolnshire, England
Corporal John Henry Smith 8/3761, DOW 22 September 1916. NZ NOK.
Private John Phillip Smith 59471, DOW 29 April 1918. NZ NOK.
Corporal John Richard Smith 12/2120, KIA 26 September 1916. NOK son of Mr and Mrs John Smith, 20 Kimberley Street, Unthank Road, Norwich, England
Private John Smith 8/4222, DOW 11 June 1917. NOK listed as John Ironside (brother-in-law), Pembroke, Otago, New Zealand. So could be from anywhere outside of NZ originally.
Private John Smith 48288, DOD 19 February 1919. NZ NOK.
Private John Smith 12/943, KIA 7 June 1917. NZ NOK.
The only one that stands out as a vague possibility for "
Private John Smith, New Zealand Regiment, died of wounds in France on the 22nd June, 1917. He was a Grandson of the late James Smith, Harewood Mill, Rulewater" is Private John Smith 8/4222, DOW 11 June 1917 whose NOK was listed as his brother in law. However, it's 11 days out in date, and we'd be basing it on spurious reasons, really, just becuase the brother-in-law is next of kin, not someone else.
My feeling is that John Hogg Smith KIA and John Hogg on the memorial are probably one and the same person. However, we'd probably need John Hogg Smith's date/place of birth off his service record to confirm it (although we only have "abt 1888 Gordon, Berwickshire" for John Hogg

).
That being said, it doesn't get us past Pte John Smith killed 22 June 1917, as John Hogg Smith was killed in May 1915. *head desk*
Allie