Hi, just come across this topic and may be able to clarify the relative points raised as I was a secondman/trainman at Gillingham 1987-91 and we had all the freight work on the island.
1) Re the MOD traffic this was indeed the first Gulf War 1990/91 and Ridham Dock was the destination point with VEA wagons being used.
2) Re the signalling of Westminster straight there was a 5 lever ground frame in a hut adjacent to the siding signal, coming from Queenborough there would be a proceed aspect on EV82 then we'd stop short of the points for them to be operated and then hand signalled into the siding, there was no actual entry signal. There were when I started 2 booked freights a day to Sheerness Dockyard which also served Queenborough, these from late 87 were Class 47 hauled. Normal procedure was to drop off any required traffic at Queenborough on the inward working then proceed to Sheerness and reverse on the centre road into the reception sidings, once unhooked it would then either be light engine to the Westminster straight for the outward traffic or Queenborough if there was none. It was not common for us to go light engine straight from Queenborough to the Westminster straight itself. There was also a trip working between Ridham & Sheerness using a Class 33 until that was replaced for a while with the 350 shunter & brakevan.
3) As far as I can recall I've never heard of the 350 & brakevan entering the internal part of the dockyard to save time etc, this would have been highly unofficial and not something I ever experienced.
4) Just out of interest there were in fact 2 travelling shunters based at Queenborough who we would pick up on our inward journeys, this was due to the amount of shunting/ground frame operations required on the branch. They normally didn't go to Ridham itself the shunting & frame there being conducted by the train guard/secondman.
Hope this is of help.