Hi
Can't help directly with Parowmas - except to recommend that you also look for associations with travelling families called Gray and Shaw in this region of the country.
The Grays also used the 'Parowmas' forename - as Posthumous, Pyramus, Parmas and variants - so there's likely to be a family link here. (From experience, it's not a name you tend to find in many other Gypsy families.)
There were also a number of instances of Shaws marrying Harrises - particularly those who belonged to the Harris travelling fairground family in Cambs, Beds, Herts. (There's a book on the Harrises called 'The Story of Harris's Fun Fairs' by Ken Page - but I couldn't see a reference to Parowmas or Moses Harris in a quick scan through this.)
I also have references to the same Shaw family intermarrying with Webbs in the mid-19th century.
On Moses Harris: I have these Cambs references gathered from parish register transcripts held at the Society of Genealogists or directly at the Cambridgeshire RO which might give you a lead - particularly the first one:
Bapt 8 Nov 1829, Chippenham, Cambs
Moses Harris son of Aaron Harris and Mary, Labourer, abode Lidlington, Cambs
Bapt 24 March 1839, Horseheath, Cambs
Benjamin Harris son of Moses Harris and Sarah, Travelling workman of Litlington. The child was born at Horseheath
Bapt 6 April 1794, Litlington, Cambs
Moses Harris son of Aaron and Sarah Harris (no other information)
Bapt 19 Oct 1788, Melbourn, Cambs
Moses Harris son of John and Elizabeth Harris, travellers, paupers
Married 14 October 1816, Haddenham, Cambs
Moses Harris bach (signs X)
Sarah Buttris sp (signs X)
Both of this parish
Witnesses: John Buttris X, Ann Harriss X, Richd Amory
From the above and from other Harris references I have, Litlington and Oakington, Cambs, look like good places to focus on.
Best wishes
Sharon