Quaker Gibbs of Burlington County, NJ

My Gibbs branch has always been a brick wall for me. My grandmother had fairly extensively researched her and my grandfather's genealogies and over the years, I went about confirming most of it with records and expanding on several branches. But not the Gibbs branch. Here's what I know.

Hope's baptism confirms her parent's names but not
mother's maiden name

Hope Gibbs was born November 3, 1805 in Philadelphia, Pennsylvania to Caleb and Isabella Gibbs. There is an adult Lutheran baptism record for her which confirms her birth date and parents names, and other records like her death record confirm her birth place. According to my grandmother, Isabella's maiden name was Peters but I haven't found any record of that and have only my grandmother's word to go on (and she is deceased so I can't ask her where she got it from). It's possible she got the name from her mother-in-law, or her grandmother-in-law and therefore the info is subject to the corruption of things being passed down the generations through word of mouth. Equally, I haven't been able to find any conclusive info on Caleb apart from the mention in Hope's baptism record.

What I did find was some Quaker records of a Caleb Gibbs in Upper Springfield, Burlington County, New Jersey and the timing is right that this could be my Caleb Gibbs, that he was originally in New Jersey and moved to Philadelphia before Hope was born. I can't find records of him in Upper Springfield after Hope's birth and to strengthen the ties between the two Calebs, I found a marriage record of Caleb Gibbs and Isabella Brannin (mis-transcribed as Browning) on April 29, 1799. Ancestry.com has the record of the marriage in Philadelphia, but this has been incorrectly indexed. Family Search has a copy of the record from the true location in Burlington, New Jersey.

Caleb Gibb's marriage without Quaker consent - lack of mention
of wife's name suggests she was not a Quaker

The trouble is I have no idea if my Caleb was a Quaker or whether he came from Burlington, New Jersey. The only links I have between them is that the Caleb from Burlington obviously married an Isabella, which matches with my info, and that there's no more Quaker records of him in Burlington County after 1800 (before Hope's birth), or seemingly any records at all of him in Upper Springfield after 1800 (though there are some Caleb Gibbs in neighboring townships). In fact, the reason for the lack of his mention in Quaker records after 1800 seems to be because there was a conflict with him and his marriage. It appears he married without the consent of the Quaker elders and he wasn't sorry for it. If this is my Caleb, this could be the reason he left Burlington (and perhaps even the Quakers) and went to Philadelphia.

Isabella's excommunication from the Quakers following
the birth of her illegitimate child

Interestingly, searching for Isabella Brannin in the Quaker records turned up a woman by that name who had a child out of wedlock in 1795 with Levi Webster. They were both excommunicated from the Quakers for it. This could be why Caleb's marriage to a disgraced woman and ex-Quaker was not approved. Isabella does not appear to have married Levi, which would have left her available to marry Caleb in 1799. Then all records of Caleb in Upper Springfield Township cease after 1800 - is it because they moved to Philadelphia, where their daughter Hope was born in 1805?

Quakers seem to be pretty well documented so I'm hoping someone who is researching Quaker Gibbs in the Burlington, NJ area might be able to help me link my Caleb Gibbs to them. It seems likely the two were one in the same, but I feel like I'm missing an affirmative link.