The local paper was the Kentish Independent, which is on microfiche at the Heritage Centre. Records do need to be sorted out; I, too, have ploughed through cardboard boxes. This is par for the course for Woolwich Borough (as was). The staff are very friendly and helpful there.
The Heritage Centre and Firepower are not in the same buildings, although they are very close by. I think some larger equipment is stored within the building occupied by the Heritage Centre. Firepower has its own archives and librarian, although you have to make an appointment.
http://firepower.org.uk/do-your-own-research/Firepower is due to move out of Woolwich in a few years' time, but current plans are for records relating to the Artillery in Woolwich to remain and be stored/displayed at the Heritage Centre and the Old Military Academy Building.
I live close to Macoma Road, if you would like a photo of the house. Also, Greenwich Heritage Centre has a Facebook page. They are gradually adding digitalised pictures of the area to a searchable database for downloading (at a price) and are open to suggestions for topics to be focussed upon.