It's quite odd to suggest any form of a new south coast route that avoids Southampton, which must be the main traffic generator by far...
Paul
You do have a far quicker route from Fareham to Romsey via Eastleigh - the line along the coast and through Southmapton wriggles. Perhaps a chord at Eastleigh to allow trains to run via Botley and Southampton Airport and rather than wriggling into Central carry on to a terminus just ahead of the wriggle. You could call it "Southampton Terminus". The back out to Eastleigh and round via Chandlers Ford.
Oh - wait - did you say it is not 1st April??