Kk7, if you read Elwyn's post again very carefully, you will see that he has said that although there is no obvious mention of your Willam's death on the headstones at First Broughshane, there are headstones belonging to families from Pollee/Pallee townland.
So, given the chap who seems to be 'your' William lived at Pollee/Pallee at time of his marriage to Lizzie, it is very possible he was related to other Armstrongs living there. In particular, as he listed his father as a William, the William and Nancy in the 1901 census, could potentially have been his parents, or even cousins of his father.
The other family groups mentioned by Elwyn are also worth checking in more detail, as well as those at Knockboy townland, as there could be links within either/both to 'your' William too (eg cousins).
If you haven't already done so, it would be a good idea to read through the whole thread again from the start, extract the various finds and suggestions, then organise these into manageable chunks to enable you to research each part more fully and effectively, thus hopefully avoiding further confusion.
You have had a lot of finds/suggestions/info given to you in a very short time today, and admit that this has previously been a brick wall for some while. It can therefore be very tempting to want to check everything all in one go, but don't rush things now. Deep breath and work through each find and suggestion step by step, attempting to either further prove or disprove as you go along.