Those intercalary chapters serve a very important rhetorical and thematic purpose. This is the story of one family, the Joads. We follow them from Tom's homecoming to the final scene as they are once again displaced. One family, one set of troubles, one story. What those "extra" chapters do is show us it's more than the Joads--it's lots and lots of people suffering lots and lots of losses and indignities and sorrows. these chapters serve to magnify one family's story into a wave of westward movement.
When Melville finished "Moby Dick" he sensed that he had taken a great risk and won. He dedicated the novel to Hawthorne and wrote to him," I have written a wicked book, and feel spotless as the lamb." Melville had completed the "circle" as described by Steinbeck. Yet, his novel was not popular and did not sell well until after his death.
So many artists feel the compulsion for self-expression that supercedes form, etc. Melville's many digressions may be frustrating for readers, but they were the outpourings of his memory and soul; for this he felt "spotless as the lamb." Likewise, Steinbeck has tremendous artistic expression in "Grapes of Wrath." Those critics who are staunch adherents to form were more negative about this novel than those who read a work of art. The title itself suggests such profuse outpouring of the soul. Steinbeck speaks to the reader; perhaps, he must step outside the narrative to do this. Leo Tolstoy ended his narrative a couple of hundred pages before he concluded his book; these last pages were reserved for his philosophic reflections on history, yet "War and Peace" is considered one of the greatest novels of all time.
To answer your question, yes I think Steinbeck did wish to offer socialism as a solution because he had written novels before in reaction to other social problems (e.g. The Pearl after the Zoot-Suit Riots in 1943 Los Angeles.) But, I also believe that Steinbeck wishes to express yearnings of his soul.
Because Steinbeck's "Grapes of Wrath" received early criticism for being most unconventional in structure, you could examine this idea (e.g.the breaks from the narrative by such chapters as the third one in which Steinbeck writes a beautiful passage of rhetoric.) Another criticism by reviewers of his time is Steinbeck's factual errors and "misleading propaganda" (remember that he was a socialist).
Critics such as Malcolm Cowley of the New Republic focused on the latter half of the book, particularly the ending. You may want to research his article and see what criticisms were made and what you could contribute to this analysis. Another critic, Edward Weeks of Atlantic Monthly, felt that the novel was one "whose hunger, passion, and poetry are in direct answer to the angry stirring of our conscience these past seven years," so you may wish to examine the sociological structure of the novel. One critic lauded this structure as not unlike such great works as the Bible and "Moby Dick."
Its seems, therefore, that the merits of this novel have been assessed from the perspective of the reader, more than that of the writer. That is, some view the book more as a work of art than as a work confined to rules of fiction. Yours is an interesting project. Once you decide which perspective that you wish to take, you can go from there. Best Wishes!
But why do you think Steinbeck himself wrote it with all these commenting chapters? Do you think he simply wanted to tell the world how to work out the best way - with socialism and part of communism?
Or do you think as he says "The circle is not closed until the trinity is present - the writer, the book, and the reader. And this works with everyone but critics (all under graduates are critics). Critics dare you to be ''great.'' But this is all after the fact. You didn't want to be great. You just wanted to write a book and have people read it. I have had some very strange criticism." that the purpose of writing it in that way was to write a book where "the trinity is present" ? And what purpose would this "trinity" have?