Hi there,
1. I really think you can rule out Clifden as being where your Driscoll's came from. I thought you have documentary proof that he was from there, but given that you don't and the extreme rarity of the surname in the county, it would be unlikely they were from there.
2. Given that you have mentioned that there are stories of Galway in your family. Maybe one of the women that married a Driscoll was from Galway

3. Yes you will have trouble tracing the exact Denis Driscoll in Cork, but I think you've a lot more work to do in Poplar and Meelish Street to be 100% sure that you are working with the right family before you even think about looking in Cork.
4. I wouldn't worry about the occupation for now. 'Seaman' as far as I'm aware can cover a multitude of jobs as indeed can labourer, as to his daughter saying that he was an Engineer on her marriage cert, sure maybe she was showing off or exaggerating, or maybe as he died quite young she didn't know his exact occupation, so I would rule out engineer as his occupation for now.
5. With cases like yours, I think the best thing to do is start from scratch with the hard copies of all documents and paperwork that you have. Start with the marriage cert of Mary and Henry infront of you, then look on all the census for possibilities for her in the 1891 cenus (search for the family in as many different ways as possible ie by surname including variations of spellings, by christian names and years of birth and places of birth, also look at occupations).
6. At this point you will probably need to invest in some certs, but in saying that you are lucky in that you search area has quite a lot of records online on ancestry.
Hope that makes sense and you have a breakthrough soon !
Tara