Platforms 1 to 6 were only capable of holding 8 carriages. The stoppers (fast to Surbiton and then all stations) to Portsdmouth and Southsea and Alton invariablY arrived at and left from platform 6. Then the next few were used by the 4-CORs on the fast Portsmouths. The main platform was platform 11 which was alongside the cab road, the Bournemouth Belle left from there as did the boat trains as a rule, although steam expresses (and also Warships) ran to and from the adjoining platforms as well. (Remember that there were the Basingstoke stoppers as well which were usually only five carriages, and then there were van trains as well). I'd say that the loco hauled trains used the range of platforms from say 9 to 14 or thereabouts. Platforms 16 to 21 were for the Windsor Lines (again only 8 car platforms.And thats exactly what happened at Waterloo.......as the train left, the incoming loco followed it.
Don't forget that during the Warship period, arrival and departure was often from different platforms: an 09 shunter would draw the carriages out followed by the Warship, each going separate ways. The shunter would then move the coaches into the departure platform and then leave, allowing the Warship to back onto the train.
If memory is correct, arrivals were at a low numbered platform, something like 5 or 6, while departures were from a high number - 19 sticks in the memory but I may have that wrong
I can't say that I remember stock being shuntd from platform to platform, but I do remember it being transforred backwards and forwards to Clapham Junction carriage sidings on a regular basis, usually by an M7 or a 5700 pannier tank until these were replaced by Ivatt 2MTs and 82XXX Standard tanks. .