Logical Punctuation II

Because the following aren't direct quotes by an individual, I believe that, per British rules, the full stop falls outside of the ending quote mark. Would a British expert assess these as being 100% correctly punctuated per logical punctuation?

(1) I hated the sentence 'It is what it is'.

(2) I like the saying 'A bird in the hand is worth two in the bush'.

(3) Amy said, 'I like the saying "A bird in the hand is worth two in the bush".'

(4) The sign at the swimming pool read 'Swim At Your Own Risk'.

(5) His email stated 'There will be a meeting on Friday, December 23rd at the Town Hall. Make sure to bring all policy updates'.

(6) Amy said, 'I hate it when he calls me a "cougar".'

Thank you.