After a few hours in the BRO:
1. The daughters of Richard HEAD (1677-1756) remain as before. There is nothing wrong with the transcript a second Ann is baptised. No Ann is buried between the two baptisms. Alternatives are:
a) Ann1 dies and is buried far away or not entered in PR Ann2 then arrives and marries at 12.
b) Ann1 surives and marries aged 27/8, Ann2 is misentry for baptism of Rachel (or second Ann is always known as Rachel).
I slightly prefer b).
2. The property at Peasemore is much clearer - about 30 acres in three pieces of land and a farm cottage and buildings known as Freelands and The Belchers plus three cottages in the village. All but the 3 cottages are sold by 1838 to some chap called GRIFFIN who lets it to Thos CLARKE (1838 Valuation of Peasemore). The cottages are owned by Richad HEAD and let to James HAMBLIN, George COOKE & Isaac LEAK). However, I cannot say for sure that the cottages and Freeland etc. were ever all owned by the same person.
3. Freeland occupied by Richard HEAD in 1755 (knew that), by Thomas HEAD in 1762 & 1768, Widow HEAD in 1774, Elizabeth HEAD (aka Widow?) in 1780 and 1787 (she dies in 1790 buried at Chieveley). On each occasion the named person is appointed an Overseer of the Poor for Peasemore always with the designation 'for Freelands' (Overseer's Book for Peasemore). It seemed to be the custom for the more significant resident rate payers to take it in turns to be an Overseer - every 6 or 7 years. New I want to find out more about Thomas and Elizabeth.
I am now less confident that Richard Head COLES moved to Peasemore abt 1816 as Richard HEAD. He may have sold the property to a sitting tenant / cousin called Richard HEAD. Or he may never have owned it - the three cottages could be all the property that was passed down the Thame / Grendon Underwood line (they seem to be worth enough to qualify for a vote).
All in all not a great day for my theory - the possibility of the 3 cottages (and not Freelands) being the property owned by Richard HEAD of Thame and passed on to his son John of Grendon Underwood means that there is an increased chance that a different Richard HEAD inherited Freelands in 1756.

Then I spent far too much time trying to decipher an indecipherable will (on film) whilst I am sure the original would be clearer it cannot be produced. Now I will waste a bit more time trying to make sense of the printout.