Sandiford also appears as Sandford, Sandover and Sandever – they sound similar if you put the emphasis on the first syllable.
The East Chinnock registers are in very poor condition up until the 1800s, and many years are missing in the 1700s as well. I'm sure there are more Sandiford entries that are illegible or missing altogether. I only looked at East Chinnock up until 1851, and in the Chillington registers I only had time to check the specific baptisms you asked about. If you hire the microfilm through the LDS I'm sure you could find more (East Chinnock and Chillington are on the same film).
East Chinnock
Marriages:[Augustin?] Sandford and Sarah [Prist?] married 11 July 1745 (the handwriting in this entry was hard to read)
John Sandford and Margaret Chalker, both of Hardington (this probably refers to Hardington Mandeville as it is only 1.8 miles from East Chinnock), married by banns 2 March 1778. Marks of both. Witness: Joel Reynolds.
John Sandover and Susanah Bicknell, both of the parish, married by banns 15 April 1781. Marks of both. Witnesses: John Sandover (probably the John who married Margaret Chalker in 1778), Joel Reynolds.
William Sandford of West Coker and Harriet Bartlett of the parish, married by banns 18 February 1800. Both signed. Witnesses: James Warry, Thomas Leach. Banns read 12 January, 19 January, 26 January 1800.
Samuel Sandever and Sarah Baker, both of the parish, banns read 23 August, 30 August, 6 September 1795. (I didn't find the solemnisation of this marriage).
Henry Sandiford and Ann Sandiford, both of the parish, married by banns 24 May 1824. Marks of both. Witnesses: William Gibbons, Joseph Purchace, Thomas Sandiford. Banns read 14 March, 21 March, 28 March 1824.
William Rendall and Sarah Sandiford, both of the parish, banns read 11 August, 18 August, 25 August 1850.
Baptisms:Thomas Sandiford, son of John and Margaret, baptised 1 March 1779
Sylvester Sandiford, son of John and Susanna, baptised 20 January 1782
[illegible] Sandiford, son of [illegible], baptised 7 February 1796 (this entry is so faint as to be almost not there at all)
Harriet Sandford, daughter of William and Harriet, baptised 19 April 1802
Sarah Sandford, daughter of William and Harriet, baptised 5 August 1810
Maria Sandford, daughter of William and Harriet, baptised 5 August 1810 (there is nothing to note whether these were twins or an older and younger child)
Thomas Sandiford, son of Thomas and Emma, baptised 17 July 1836, abode East Chinnock, father's profession Carpenter.
Emma Sandiford, daughter of Thomas and Emma, baptised 13 December 1840, abode East Chinnock, father's profession Carpenter.
Henry Sandiford, daughter of Thomas and Emma, baptised 15 October 1843, abode East Chinnock, father's profession Carpenter.
Burials:Ann Sandiford, died 11 September 1777
Margaret Sandiford, buried 14 May 1809
Sarah Sandiford, buried 28 July 1819, age 47
Henry Sandiford, buried 3 January 1828, age 22
Emma Sandiford, buried 23 March 1845, age 5
Ann Sandiford, buried 5 April 1851, age 87
Henry Sandiford, buried 13 April 1851, age 82 (these are consecutive entries and are noted as husband and wife; I may have mixed their ages up)
Chillington
Baptisms:John Thomas Sandiford, son of Thomas and Amy, baptised 12 November 1826, abode Chillington, father's profession Carpenter.
Samuel Sandiford, son of Thomas and Amy, baptised 30 September 1827, abode Chillington, father's profession Carpenter.
Sarah Sandiford, daughter of Thomas and Amy, baptised 28 February 1830, abode Chillington, father's profession Wheelright.
Samuel Sandiford, son of Thomas and Amy, baptised 5 January 1834, abode Chillington, father's profession Carpenter.
