Hi Barbara,
What an amazing challenge and great cause. I would love to hear more about this trip, the RBH is dear to me as I was born there!
Let me start by saying I have no experience of cycling in this part of France, the only bit I have done is from the north coast to Paris. However in an effort to help I have looked at the map and it is clear how you have ended up on the N7, it is the logical route. The real major towns along the way are arranged along the east of the main rivers, I wonder if you would be better off on the D routes to the west of the rivers?
Maybe you have researched it already but perhaps crossing at Mondragon and then continue north west and cross further west at Pont-Saint-Esprit? It might add a bit of distance but then you have the D86 tracking north, it won't help with the wind but it will be quieter than the Route National N7.
It will also allow you to avoid Montellimar which looks like a massive (and difficult to navigate by cycle) type of large town.
Further north near Le Peage de Roussillon the D86 leads on to the D1086 and then the D386 passing through some national parks which has got to be nice, all of these roads keep tracking alongside the river. The D386 leads to Brignais which then allows you to choose your route in to Lyon for the last 10-20 miles.
Let us know how you get on and good luck.
Barbara, good luck and be careful!
