Its quite appealing to go from sea to sea, but the reality appeared to be that the first few days from Trieste would be rather dull dirt roads and woodland trails, so I've decided to start on the edge of the Alps proper at Cerkno. You can get there by bus from Llubljana which is accessible by train from the UK, so I'll start there after a 2 day journey.
The route breaks down as:
Karnische Alps - Follows the border of Italy and Austria, initially on wooded hills, then Limestone mountains with some via ferrata
Dolomites - A challenging link up of as many high level via ferrata as I could find including several of the major summits and mountain groups such as the Sextner Rotwand, Sorapis, Tofana, Langkofel, Sella and Rosengarten.
Ortler to Bernina to Disgrazia - Mountaineering linked by high Alpine paths. Possible ascents of the giant Ortler, the Piz Palu - Piz Bernina traverse and Monte Disgrazia, followed by a high level traverse under the Piz Badile.
Roof of Switzerland - Monte Rosa peaks over Lyskamm and Breithorn.
High Italian passes and a few 3000m+ summits from Valtournenche to Courmayeur passing South of the Valais Alps and Mont Blanc ranges.
Begins on the GR5 to the Vanoise National Park, but soon abandons this for a more high level and rough route taking in 3000m+ summits in the Vanoise, Queyras and Mercantour national parks to the Mediterranean including an ascent of Monte Viso.