Once you have a list of reasons, you need to decide how you are going to prove or disprove each one. In this case, finding which church or churches they were most likely to have got married in and looking through the parish registers until a record is found would prove either of the first two reasons. After you have decided how to prove/disprove each reason, the next step is to start with the easiest to eliminate and go through them until (hopefully) you get a resolution. In this case, I started with the middle names as surnames, as I could easily look through the marriage indexes online. This was quickly eliminated and I moved onto seeing if one of them was already married to someone else. Bingo! This was the reason; the man was already married, not only that, he and his wife had three children. I was able to verify that this was the right person with other documents.
I have successfully demolished a few brick walls with “alternative scenarios”.
Widespread literacy only became the norm in many countries in the late 19th and early 20th centuries, so, often a cleric would change the spelling of a name when recording a vital event as he wrote down what he thought he heard. My own name, McGowan, is often spelt MacGowan, McGown, McGow or is anglicized to Gowan, Gow or even Smith (the literal translation). So I always look for all possible spelling variants.
Look for clusters
Before the 20th century there wasn’t a great deal of mobility. Of course, seismic events like the Irish potato famine or the Highland clearances forced people to move to the cities or emigrate, but when this did happen people often did this with members of their extended family and neighbors from the same community. So if someone disappears, say after the 1851 census, it often pays to look for other members of their family or community (clusters) in later documents like the 1861 census. You might find some clues. Elizabeth Shown Mills calls this the FAN principle (Friends, Associates, Neighbors); you can find more information about it here.
Finally, illegitimacy is another common cause of brick walls. See How to Deal with Illegitimate Ancestors for some tips in looking at this problem.
I hope some of this can help you with your brick walls.
If you’d like some further reading on problem solving and brick wall demolishing; check out these books: