We rode from Grenoble to Sospel, effectively the lower half of the Route des Grandes Alpes, in a day. This coincides with much of your route. We added in a blast up and down Alpe d'Huez and Col de Galibier for good measure.
That's 225 miles, Autoroute says 5 hrs. In reality, we left at 09:30 and arrived in Sospel around 9 pm. We stopped for lunch, numerous photo stops, coffee and ciggie breaks and petrol. I suspect we could have got it down to 7 or 8 hours easily enough.
We had good weather, sat nav to stop us getting lost, and a bloody good argument in the evening as to which was the best pass! (Either Vars or Bonnette was the outcome, although Turini dropping into Sospel was a highlight as well.)
So, I reckon your route is achievable easily enough, just depends on how much time you want to spend admirign the scenery as well as charging up and down the mountains.
I suppose we want to see as much as possible we can always go back to our favourite bits another time. Always differcult to know where/what to do when it's a new area!
I am going to take it, we can do it provided the weather is good



