Do you really think it is going to make much difference when it is in place? I know a lot of pilots who frequently use the Stoney Cross/Bealieu leg and most of them, including myself, have always listened out to Bournemouth rather than Solent. In my experience there is not a high probability of either service warning you of other traffic but Bournemouth would be a better bet. On a visit to their Tower I asked who I should listen to and they said either would do but please don't fly close to the Bournemouth boundary at 1900' (legal) in a westerly as it stops them using the ILS for 26.
Oddly, the only infringement I know anything about in that area was due to distraction which was partly contributed to by Bournemouth unexpectedly requesting the pilot to change to Solent as he was getting closer to their boundary.