Last time I had a subscription, the online BNA (British Newspaper Archive) did not have coverage back that far. However, as you have discovered, there were Wexford papers back to 1820 and earlier, just not online. I would suggest:
- Checking current BNA coverage, they might have added.
- British Library should have a copy. I don't know if they have a service to check particular editions.
You might wish to donate the two copies you have to the National Library of Ireland.