li,

the way i speak doesn't include 'pit' & 'peat' being pronounced homophonetically.

my perception of this type of received pronunciation is more akin to s. african english.

going back to topic, i asked my elder sister, who's 70+, where our family learned 'incy wincy spider' from.

she said during ww2, there were a lot of foreign armed services personnel stationed in our local area, including many americans. she thought an american friend was the source of this rhyme because she remembered him reciting it to herself and my brother who was about 2 at the time.

if this info is correct, if 'incy wincy' is really from the states, then its 'think again time' as regards your hypothesis.

hope this is useful?

cheers

mr h