Felicia,
You could certainly work your way through the records in PRONI if you have the time and patience. If you know the McWilliams family’s exact denomination that will reduce the search quite a bit. It’s worth bearing in mind that not all church records have survived. Some have been lost for various reasons eg many Church of Ireland records were destroyed during the 1922 civil war in Dublin (where they had, ironically, been sent for safe keeping) plus some others in Belfast churches were destroyed by German bombing in WW2. And then there were a few Ministers who just didn’t bother keeping records.
There’s probably about 150 churches in Belfast, plus another 200 or so in a 20 miles radius of the city, but they weren’t all open in the period you are interested in say 1819/1822 and some have no early records for the reasons I mentioned, so that will reduce the search a bit. It’s still a lot of records to work through though.
Looking at the 1901 census for Antrim and Down, of the 621 McWilliams in it, about 310 were Presbyterian, 150 RC, 150 Church of Ireland, plus a handful of Methodists, Covenanters and Unitarians. If your family was RC, their records are nearly all on-line on the nli site: http://www.nli.ie But for the rest, most of the records are not on-line and you need to work your way through them at PRONI.
Though PRONI’s actual church records are not held on-line, they have a catalogue which lists what they have got and so you can take stock of what the task involves. In most cases the records are on microfilm and you’ll see a reference number beginning MIC for those. They also have some in paper format and they usually have a file prefix like CR or T or D.
http://www.proni.gov.uk/guide_to_church_records.pdf
There’s the occasional church where PRONI don’t have the records. That church either declined to let their records be copied or they simply weren’t available in the 1980s when this collection was put together. Those records say: ‘in local custody” and so to access them you need to contact the minister/Vicar etc of the parish.
All the records for Belfast have been indexed together. Outside Belfast you need to search by parish. Here links to maps showing all the parishes in Cos Antrim and Down.
https://www.ancestryireland.com/civil-parish-maps-for-ulster/civil-parishes-of-county-antrim/
https://www.ancestryireland.com/civil-parish-maps-for-ulster/civil-parishes-of-county-down/
Rootsireland has some church records for Cos Antrim & Down on-line. If you are a subscriber, and search by county, you can see what records they have (they don’t always cover all years). You could then use that to eliminate those churches from your search.
I’d be a bit cautious and flexible about the dates and years of birth that you have. Folk in Ireland in the 1800s didn’t celebrate birthdays and often had little idea of exactly when they were born. So when officialdom asked them for a date of birth they sometimes just made one up. So search a year or two either side of the dates you have.
You say that James may have lived in England prior to his departure for the US. That’s quite possible. Ireland has few natural resources and so the industrial revolution largely passed it by. Many folk from Ireland therefore went to England or Scotland to work for a while before later moving again to North America, Australia etc. It's called stepped migration.
On the other hand, many Irish emigrants left from Liverpool because there were far more sailings from there than from Ireland itself. Liverpool was a sort of clearing house for migrants from all over Europe, bound for the US, Canada and elsewhere. So it had almost daily departures whereas there might only be one or two a month from Ireland. There was quite a lot of competition for the trade and many shipping agents threw in the cost of the short journey from Belfast to Liverpool free as part of the package. And James may just have met his English wife on the voyage. Many couples met like that. If you were young, single and kept in close confinement on a ship with groups of other single people, with nothing to do for 3 weeks, then friendships and relationships were easy to start.
If going to PRONI, take photo id (ie your passport or driving licence) on the first day to get your reader’s ticket (takes just a couple of minutes). Late opening is Thursday, when it’s open till 9.00pm.
Can’t really help you with the DNA mystery. An adoption or some other non-paternal event, at some time in the past might be one explanation.
Good luck anyway.