According to Humphery-Smith:"Armigerous Ancestors", the 1612-14 St George visitation of Cheshire is contained in College of Arms ms C6, the British Library's Harleian mss 1070, 1535, 2187, and Add. ms 29783.
Wagner: "The Records and Collections of the College of Arms", 1952, 82, states that C6 is the original in St George's hand with signatures but that Harl. ms 1070 has some of the rough pedigrees with signatures.
The BL mss catalogue shows Add. ms 29783 is "A COPY of ye visitation Book of Cheshire ann. 1613, taken 1752 by R[obert] S[myth, M.A., Rector of Woodston, co. Huntingdon] from one in y e Possession of Tho. Wotton, of Point Pleasant in Kingston, Surr., Gent.;" with "an alphabetical list of ye Gentrys arms Blazon'd." Paper; 1752. Folio.
This last phrase may indicate a copy of the arms you seek - but of course in the same location.
Beyond that, I do not know which ones copy which.
Incidentally, Lancashire & Cheshire RS, vol. lviii, 1909 is also available as Harleian Soc. vol. lix.
Derek Howard