Well, I've tried to help but nearly drowned in detail myself!

Charlie

According to Google maps, Failsworth and Oldham are about 4 miles apart, while the Cathedral (which was only a Collegiate Church at this time, but it's easier to write "Cathedral"!) is about another 4m in the other direction from Failsworth. For various reasons, a huge number of the marriages in the Manchester area took place in the "Cathedral".

I don't know what records are in FamilySearch for the Manchester area - when I was researching stuff in this area, I used Ancestry because they do have most of the churches. I would also add that Lancashire OPC on http://www.lan-opc.org.uk/ have a lot of transcripts - but not all. And the FamilySearch Wiki on Lancashire has a huge amount of stuff saying what can be found where (start with https://www.familysearch.org/wiki/en/Lancashire_Parishes )

What I would do is start by looking for possible marriages. Note that your baptisms are horribly close to the 1754 dividing line for marriages. Before that, marriage records in Parish Registers tend to be one-liners, usually in the same registers as baptisms and burials. After that, they are much more detailed and in their own registers. (Bishops' Transcripts for post-1754 can be either one-liner summaries or detailed but are usually on the same sheet as baptisms and burials.)

The next thing to be aware of is how Ancestry split the images (if you're using it). They have collections for Manchester "Cathedral", collections for Manchester Diocese excluding the Cathedral, and "the rest of" Lancashire. Those collections contain the Parish Registers, but the Bishops' Transcript copies seem to be usually found in "the rest of" Lancashire collections, regardless of where the church was.

To find these *if* you use Ancestry, you should go to the Ancestry Card Catalogue and first search on Lancashire and then on Manchester in the title field. I found these that might contain data for you:

Pre-1754 marriages:

Manchester, England, Baptisms, Marriages and Burials, 1573-1812 (Cathedral)

Manchester, England, Church of England Baptisms, Marriages and Burials, 1541-1812

Lancashire, England, Church of England Baptisms, Marriages and Burials, 1538-1812

Post-1754 marriages:

Manchester, England, Marriages and Banns, 1754-1930 (Cathedral)

Manchester, England, Church of England Marriages and Banns, 1754-1930

Lancashire, England, Church of England Marriages and Banns, 1754-1936

Searching for likely marriages in each of those 6, I found just 3:

1) Name:   James Roy

Marriage Date:   29 Jan 1753

Parish:   Manchester, Lancashire, England

Spouse's name:   Hannah Pearson

Register Type:   Bishops Transcripts

This is actually James Royley in the "Cathedral" parish register of the same date, so can probably be discounted.

2) Name:   James Wroe

Gender:   Male

Event Type:   Marriage

Event Date:   5 May 1756

Parish:   Manchester, Lancashire, England

Spouse:   Hannah (it's Hannah Thomas in the image)

Register Type:   Bishop's Transcript

I can't see this in the parish register for the "Cathedral" because the guys filming it seem to have turned over two pages at once!! And it's not on LancashireOPC either, so I have no idea of the detail.

3) Name:   James Wroe

Marriage Date:   16 Apr 1757

Parish:   Manchester, St Mary, St Denys and St George (i.e. the "Cathedral")

Spouse's name:   Hannah Wolstenholme

James is a weaver from Moston, Hannah is from Failsworth.

So my working assumption would be that there are two James and Hannah marriages. Looking in LancashireOPC (because that's all one collection but is incomplete), that seems to have a series of baptisms at Oldham from August 1757 to Jan 1769. James is a weaver throughout, resident in various places - Failsworth, Lowerhouse (there is a Lower House in Oldham according to Google) and at least one Lane that I guess may be in Oldham. It looks to me like there is no reason not to believe this is one family. And surely James Wroe and Hannah Wolstenholme must be this family because of the Failsworth reference?

LancsOPC also has a 1777 Thomas Wroe at the "Cathedral" in LancsOPC. That's nearly 9y after the Oldham baptisms - I'd be inclined to presume this belongs to the other James and Hannah.

In Ancestry's "Manchester, England, Baptisms, Marriages and Burials, 1573-1812 (Cathedral)" I found a number of other James & Hannah baptisms. For instance:

Hannah Wroe 28 Jan 1759

Compare that to the one at Oldham (from Lancashire OPC):

 6 May 1759, Joseph Roe

Now, assuming that someone is baptised reasonably close to their birth, then that can't be the same family. So again, it's saying that we have at least two families of the same name.

There are other James & Hannah baptisms - as you probably know. E.g. there are BTs from Newton chapel in Ancestry's "Lancashire, England, Church of England Baptisms, Marriages and Burials, 1538-1812". For instance, I saw James Wroe on

20 Sep 1772, where his parents lived at Failsworth.

To do the baptism analysis properly, if you use Ancestry, you need to look at the 3 collections:

Manchester, England, Baptisms, Marriages and Burials, 1573-1812 (Cathedral)

Manchester, England, Church of England Baptisms, Marriages and Burials, 1541-1812

Lancashire, England, Church of England Baptisms, Marriages and Burials, 1538-1812

and look for the baptisms in there. Some of those will include what I've already highlighted above. Then you can do things like compare the dates like I did for the 2 1759 baptisms, to decide that those 2 families must be separate. If the Newton baptisms follow on the end of the Oldham baptisms, with no overlap, then, given that we only have the 2 marriages, that would suggest it's the same family.

Good luck - I'm afraid that you have to do the hard work comparing one set of results to another to see if it's one family or two. It might be three if there's an incomer, of course, but the fact that there's only two marriages means I'd start with that idea and try to break it.

Not Phil but I think you need https://www.familysearch.org/wiki/en/A_Comprehensive_List_of_All_Pre-1851_Manchester_Parishes_and_Chapelries - the link above had 2 http prefixes, somehow.