1. We cut out the stretch across Chamonix, from Argentiere to Les Houches. That's the most developed stretch of the route and while i am sure on the high routes it would be spectacular, there is also a main road right up the valley with regular bus service and lots of car traffic and pretty ordinary villages. We also were staying in Chamonix before and after and so could get a sense of this area outside of the TMB.
2. We started by taking the cable car ski lift up from Les Houches to Bellevue/Col de Voza. That saved...I don’t know. Several hours.
3. We planned to take the local bus across les Contamines. The route drops you in the middle of town and instead of walking the X km to the end of the village, we planned to take the free local shuttle bus to Notre Dame de la Gorge, where the route really starts up again.
Note that a) the local shop in les Contamines closes at lunch so if you want picnic supplies, grab them as soon as you arrive in town (I think it closes at 12pm.
Also, the shuttle bus driver takes a break for lunch too from noon til 13h45. We were stranded in the main square for our picnic (which was OK). Check the bus schedule. Here is a summer (ete) schedule from 2014. check again for 2015.