Why dont you go direct - it is very unlikely you will be refused a Southampton / Solent transit.
I would ask for a zone entry at Hanky - you might find they vector you around a little so be prepared for that. If they refuse you the transit skirt around the zone down to Stoney Cross. Alternatively you could keep east of the zone and along the coast which is very scenic. (Of course I appreciate you might want to go some other way for the scenery or experience which is fair enough).
No problem at all with the Flying club "handling" you at Bournemouth - they are a good bunch and parking alongside all the slowly rotting military hardware is of interest. Mind you, if you want to get anyware (like the main terminal or just off the airport) its a real trek!
As you know its not cheap.