I see your McCaskie surname derived from his, i.e., that he is your direct patrilineal ancestor, so absolutely the first thing I recommend is a BigY-700 test at FTDNA.
Otherwise, the year 1845 is a hard brick-wall by itself for most Ireland researchers, so you have done better than most by getting back to Edward. My first suggestion would be to search the Registry of Deeds in the hope that he leased some land (assuming a schoolteacher then wouldn't have been a landowner, which would be even better).
I just searched the Registry of Deeds transcription project for Caskie and turned up nothing. But most deeds have not yet been abstracted and put there, so you can look through the registry itself. Do you know the townland where he lived? That would be most helpful.
My main other suggestion would be to try using autosomal DNA. You have to get lucky with tracing a *specific* line into the mid-1700s, but I think a lot of people can trace *some* lines back that far with a good enough tree, and you might get lucky and find one of those lines is the Caskie line.
