My ideas would be as follows:
Firstly, reintroduce the Waterloo to Southampton semi-fast, the equivalent of the former xx39 departure. Doesn't have to go all the way through to Bournemouth or Poole, another service could cover that, depending on what makes sense operationally. Would give Eastleigh 2tph to Waterloo again, something it formerly enjoyed since 1990, and improve connectivity between say Southampton and Farnborough. Add a Woking call to the service if possible, one unusual feature about this service was that it skipped Woking, which doesn't really make sense for a service aimed at least partially towards connectivity between intermediate stations. Perhaps it could make a Fleet call too (see below).
Make Beaulieu Road a call on all stopping services on that stretch. I realise it's only small - but it's useful at weekends and even weekdays during high summer. Costs very little - if some services call, you may as well get everything to call. It's presumably the same path every hour.
Ensure that the Brockenhurst to Bournemouth stopper connects at Brockenhurst with the Waterloo fast which skips New Milton, Christchurch and Pokesdown - thus giving said stations an even-interval service. This was one of the oddities post-2004, IIRC. If that means it has to become a Brockenhurst-Bournemouth/Poole shuttle, so be it.
Re-jig the Alton and Basingstoke group of services. One thing about the 2004 timetable was the significant slowdown of the Alton services prior to then: in 1997 for example Alton was reached from Waterloo in just 1hr02.
Perhaps, given Farnborough and maybe Fleet would get 2tph fast from the Portsmouth via Eastleigh and the re-introduced Southampton semi-fast, transfer of the West Byfleet stops from the Altons to the Basingstokes could be considered, accelerating the Altons (but admittedly slowing the Basingstokes, but maybe not such a big deal if Farnborough and Fleet get 2tph fast as noted). Additionally, give the Alton a better path so that it's not waiting outside Woking to allow the Portsmouth fast to pass.
As for the Portsmouth Direct, this depends on whether reintroducing 4tph to Guildford is a possibility. If so, I would simply re-introduce the 2004 pattern but perhaps call one of the two fasts at Clapham Junction if possible.
If on the other hand 4tph to Guildford is not in the plan, perhaps they could make the best of the restricted service by moving to something akin to the old 80s pattern, with 2 fasts and 2 "semi-slows" to Guildford, one of these "semi-slows" then being looped there and proceeding to Portsmouth behind the following fast, calling at all stations. This could have the advantage that the "semi-slows" could take up the Walton, Weybridge and West Byfleet stops from the Basingstokes and Altons, speeding up both. As for the fasts, one would call at Farncombe and the other (the one looped by the slow) would not call, which AFAIK is the same as now. Presumably 2tph evenly spaced at Farncombe albeit with a change in one case would be preferable to the current 15/45 min pattern. Perhaps, depending on whether 2tph properly-fast services to Portsmouth are desired, the Farncombe-calling service could also call at Liphook and Liss... just like the old days.