Cheran,
You say, "So my quandry is still whether James Hogg can be Elizabeth's father." Not strictly correct, it should be, "So my quandry is still whether the Ettrich Shepherd can be the GLS Elizabeth's father." Personally I do not think there's a snowball's chance in Hell.
However, in the HW site
http://freepages.genealogy.rootsweb.ancestry.com/~hughwallis/IGIBatchNumbers/CountyGloucester_(N-Z).htm#P you will find that Painswick has many extracted entries for Hogg so it would not be unexpected to find some Elizabeths.
The fact that one Elizabeth is not there might be because the data had been in an extracted LDS batch but was used by an LDS member in a submission. The submitted entry might even be a fairy tale and does not, as you have found, give her father's name although it gives her birth/baptism as Painswick - perhaps she was base born.
What you need to do and there is no other way, in order to find her father's name if her bap. is there and it's given, is to hire and search the LDS films of Painswick's church records, viz:-
LDS film No.595449 Independent t Church records 1780 - 1837
LDS film 425488 C of E's BT's 1570 - 1812
LDS film 855629 C of E PR's 1548 - 1888
The cost will be £7.50 per film and you'll have three months in which to search. Church records sometimes give info. such as "father reputed to be . . ."
I have recently found a shortcoming in Horsley's BT's by a search of the PR's so it would be adviseable to search both if you find nothing in the first search and of course, if the Elizabeth's father is given as James it proves nothing.
As Genuki says -
http://www.genuki.org.uk/gs/#Work - working forwards from a famous figure in history in the hope of finding a family connection is rarely profitable.
Regards
Chas