JT has answered your question on blocking....nothing else I can add.
However, I was watching "About Your House" with Bob Yap this last Saturday on my local PBS station, when he showed something I'd heard but never seen, and may be relevant to what you are attempting to do.
He showed a house that had had cellulose insulation blown into wall cavaties using small holes a couple of years prior. The paint on the siding of this house was peeling badly and most surprisingly, Bob reached into one of the small blow-in holes and pulled out a few pieces of the cellulose insulation, and it was soaking wet....he squeezed water out of it!! He said this is because a vapor barrier was not put up between the living space and the blown in insulation, and that in the winter, the inside warm moist air, that used to infiltrate the wall and then be diffused out the drafty siding was now being trapped by the insulation, where the moisture would collect and, I believe, be transferred to the (probably) unprimed inside of the siding boards, thus pushing the paint off the outside.
I don't claim to have any good working knowledge here (I've never blown insulation into a wall cavity) and I really don't have an answer to this....except that you may want to research the best method of putting a vapor barrier on your interior walls. An insulation contractor may be able to assist you here, or perhaps someone on this or the TOH board may have some ideas. I'd offer a couple but they would be just guesses (a special oil based paint perhaps??)...probably best to hear from someone who really knows.