Yep, you can add on a visit pass to a OWE trip, I've done this several times.

For shopping and mileage, DXB is a good choice.

If you haven't been to NCE before, go. IMHO, a car is not the best choice for NCE. Driving is tough in Nice, and parking is eaither expensive or nonexistant. The train can get you to most of the small beach towns along the coast, and Cannes. Monaco is a short train ride the other way - both are very easy day trips and fun. To get a better feel for Province, head to (and stay in) Aix or one of the other local communities. I would say the south of France, except Marseille, is significantly safer than FCO. NCE is not good for shopping.

The train from NCE to Paris is fast and, if you buy it in advance, cheap. From there you can fly to EDI as you noted, a beautiful and vibrant city.

If you've been to FCO already and don't have a burning desire to go back, why not try something new? Eastern Europe offers some interesting sights and shopping, and the mileage from LHR isn't bad.