If you can get a map of downtown Halifax, you will see that Agricola St is very close to the Garrison Grounds, York Redoubt and Citadel Hill which would be the area where the battalion would be at. Citadel Hill is just off Brunswick St at the top of the hill overlooking the harbour. I'm not sure where the old police station was in Halifax but the new one is very close to the citadel as well.
From memory so I may miss a street, Brunswick St, Agricola St., Barrington St, Granville St., Hollis St, Bedford Row, Lower Water St are all parallel to the waterfront. (Probably not in the right order) The old post office was on Bedford Row. The navy dockyards are off Barrington St closer to Bedford Basin but within walking distance to downtown Halifax. The navy base Stadacona is located between Barrington and Gottingen Sts. also within walking distance.
I think you should contact the Halifax Library and see what they may have that could help. Also, contact Trinity Anglican church to see if the marriage did take place there. I'm not sure what records they hold but they probably know where the records are if they exist. The church records may be held at the Nova Scotia Archives.
The catholic cemeteries that I checked were Mt Olivet, Heavens Gate and Holy Cross. A lot of Shea's buried there but not Thomas and Mary. I do think the Thomas and Mary Shea on the 1881 census may be the correct ones but then they disappear.
Good luck. Val