In 1851 the same William Twiss (judging by name of wife and children] is present on Haydock Lane as a farmer of 11 acres. His age is 41 [dob 1810]. He is in the same position relative to neighbours as in 1841 (Twiss, Turton, Dierden, Greenall/Greenhough. On the tithe map the latter two are located at the north end of Haydock Lane, and in the 1851 sequence they are located just before Mill Fields Lane which is at the north end of Haydock Lane. All of this evidence from the censuses places William Twiss at the southern end of Haydock Lane, which fits with the 1838 tithe map.
There is a baptism: 1810 St Helens for William Twist, father Thomas Twist.
There is an 1830 Prescot marriage to an Elizabeth Leavesley which may fit (he is a collier)
The family is still on Haydock Lane in 1861.
There is a death in Dec 1869 William TWISS farmer, Haydock with a probate naming widow Elizabeth and brother James, engine driver.
(I'm just giving outlines here because I suspect that you will have all of this already. The main point is to establish that this William TWISS is the William TWIST located on the tithe map.)
Note that this William Twiss cannot be the father of Thomas Twiss, widower who married Jane Spencer in 1856 because that William Twiss is recorded as deceased.
We’re cooking on gas here, Alan!

Brilliant work on the tithe maps. Thank you so much. What you've learnt and shared in this thread really is invaluable to me.
The 1810 William TWISS is a son of one of the brothers from the original group of brothers that I highlighted (Thomas b 1784).
I’m going to add some
TWISS / TWIST family details to this post. I think it will be helpful and handy to anyone with an interest in any of the family names mentioned.
T = TWISS / TWISTThomas T b. 13/12/1753 m. Sarah KNOWLES b. 10/02/1759
I don’t have an exact place of birth for either Thomas or Sarah, but it was very likely Haydock.
Thomas and Sarah’s children:1. William 1776 - 1782. Died age 5
2. Ellen 1778 – 1833 m. William BANE / BAINES = 9 children
3. James 1780 – 1854 m. Sarah GREENALL. I don’t know if James had been married before Sarah or if he’d only married late. He was 53 when he married Sarah. I haven’t found any children for James.
4. Mary 1782 – 1849 m. Thomas NAYLOR = 11 children
5. Thomas 1784 – 1851 m. Ann KNOWLES = 11 children
6. Ann 1787 – 1827 m. Peter DIXON = 4 children
7. Joseph 1789 – 1866 m. Mary BROWN = 13 children + 1 illegitimate child with Betty FORSHAW
8. David 1792 – 1852 m. Mary DIXON = 3 children. Widowed then m. Ann PIMBLETT
9. John 1797 – 1806. Died age 8
10. Hannah 1800 – 1871 m. Abraham SIMM = 7 children
11. William 1802 – 1839 m. Betty ROTHWELL = 3 children
I’m descended from Ellen T b. 1778 & William BANE / BAINES through my maternal line.
I’m descended from Thomas T b. 1784 & Ann KNOWLES through my paternal line.
The children of Thomas T b. 1784 & Ann KNOWLES:1. John 1807 - 1807
2. James 1809 - 1809
3. William 1810 – 1869 m. Elizabeth LIVESLEY = 8 children
4. Ann 1812 – 1847 (my ancestor) m. Charles FORSHAW = 7 children
5. Thomas 1814 – 1836
6. David 1819 – 1867 m. Jane FAIRHURST and m. Ellen ALLNATT
7. Edmund 1821 – 1849 m. Ann HARRISON
8. Joseph 1823 - 1824
9. Catherine 1824 - 1825
10. James 1826 – 1902 m. Anne CRITCHLEY
11. Marcus 1830 – 1830
Children of William T b. 1802 and Betty Rothwell:1. Thomas 1827 – 1892 m. Ellen BANE / BAINES and m. Jane SPENCER = 5 children
2. Jane 1831
3. William 1834
Sticking to William T b. 1802 for a moment.
I now feel I have the correct death for him:
24th October 1839, Newton, William TWISS, collier. Cause of death: “Affection of the Kidneys.” Death registered by Jonathan ROTHWELL, present at the death, Newton.
I think Jonathan ROTHWELL must be a relative of William’s widow, Betty, nee ROTHWELL. The 3 children I have for William and Betty were all born in Newton. On the 1841 census, a widowed Betty and her 3 children are living in Newton Common, which is the Haydock side of Newton. There were coal mines sitting on the boarder between Newton and Haydock, so this all feels like a fit.