I think we can confirm that Thomas belongs to the William Paice and Mary Heading family.
I wish I could find supporting evidence!
The Will of William PAICE HRO ref: 1829A/51 Cabinet Maker of Basingstoke mentions wife Mary, and sons George & William.
Although he had held a fair bit of property, including business premises which had passed to his sons, his remaining estate was sworn not to amount to £300. [Burial 31 Jan 1829 aged 62]
The Will of William PAICE 1843A/090 Cabinet Maker & Upholsterer mentions wife Mary, brother George, son Charles and other children [presumed females] not mentioned by name! Admon was granted to Charles, the surviving executor, 17 Nov 1843, amount under £3,000.
Charles died 10 Dec 1860 and his Will mentions wife Elizabeth Mary; Cousin Henry Shepherd PAICE of Curridge [Chieveley] in the County of Berks, Gent., [Uncle George's son]; Brother-in-law Edward HAYES junr of Andover, Draper; and mother Mary PAICE. Effects under £4,000. This Will was on faded microfilm and very difficult to read. However, if Thomas had survived I would have expected a mention in his father's and/or brother's will. At my next visit to HRO I will request to view the original document that was filmed in order to discount the possibility I might have missed other names, which I doubt.
Amongst the Basingstoke burials:
02 Oct 1824 Thomas PAICE 2 yrs 7 mos
21 Feb 1829 Jane PAICE 3 wks
On 01 Aug 1862 Mrs Charles PAICE's request was agreed that her name be transferred from London St Congregational Church, Basingstoke, to the books of the ch. worshipping in East St., Andover.
I think we should widen the net to include other parishes on the North Hants/Berkshire borders. There is someone doing a one-name study on the PAICEs who might have encountered some interesting records.