What I'm suggesting is that the Brighton services are a shuttle, whilst the other destinations are served by the other services. Although there's no reason for them to only serve one location.
For example:
London Brighton (then in its shadow a Brighton towards the West service, say Brighton Portsmouth)
London, Southampton, Bournemouth
London, Brighton (Brighton, Southampton, Bournemouth, Poole).
London Portsmouth
London, Southampton, Bournemouth, splits to become the slow/semi fast services to Weymouth
London Brighton (Brighton, Southampton, Salisbury)
London, Portsmouth
(Repeat for the other half hour of the hour).
That's 6tph to Brighton, 4tph to Portsmouth and 4tph to Southampton from London.
The existing services which currently serve Southampton could become stopping services between Southampton and Basingstoke (the biggest inconvenience would be to those going to/from Winchester or Southampton Airport Parkway, although the impact to those from Winchester would be 1 extra stop, so hardly very big).