Sorry, I can't add any more information than you have already collected. I have wondered about the name "Powell". It seems to have been accepted by others researching Jane Hollingshead and entered onto family trees as Jane Powell. But I have only once found that form on any of the original material I have uncovered.
On the bounty migrant lists from the NSW state archives it is given as Jane Poel when listed as an unmarried female immigrant, from Co Tyrone, parents John and Ann, brough out by Francis Reid and under the protection of Patrick McGuiggan. However the corresponding sheet for Mc Guiggan gives her name as Jane Pole.
Further to complicate the matter a search of the passenger list of the Broom 1842, show 2 Jane Ps.
1. Jane Powell aged 22, farm servant, protestant, daughter of John and Ann, and next in the list is a
2. Jane Poel 17, a nursemaid, protestant, daughter of William and Ann who came under the protection of her brother James, also brought in by Francis Reid. A cross -check of of the 2 index cards for bounty migrants show a Jane Poel and James Poel 22, both from Moy County Tyrone, both the children of William and Ann. So it would appear that I have just added to the problem rather than solving it.
'On the marriage certificate v 1845 611 30B she if Jane Poel. On her daughter Elizabeth's marriage to Charles King in 1868 she is Jane Pool. On Joseph's death certificate in 1882 her name is Jane Pole. On her own death certificate in 1887 her parents are "not known" to the informant her son George. On Elizabeth King's death certificate in 1916 her name is Eliza Jane Poole.
I am sure you are aware that others are researching this line and there is quite a lot in the Australian data bases - though no one seems to have got back to the Irish roots. I am a descendant of Jane and Joseph Hollingshead through their daughter Elizabeth b. 1845: then through her daughter Mary Jane King b. 1870, my g-grandmother. If you do have luck with this search, I would love to know the answer. With more Irish records coming online, maybe one of us will solve the problem