Child - I can see Frodo basically doing those things, but he seems to retain his basic "hobbit-ness" in your theories, and I can't really see that as being the case. He may have played this part for Bilbo, but after his passing, Frodo would have had to expand his horizons, so to speak, in order to truly fit in his new role as a halfling among Elves and Maiar.
I can see him absorbing as much of the lore and culture of the Elven-kind as he could, becoming a scholar in a way that was unavailable to him while living in the Shire.
In order for him to sustain any kind of friendships with the Elves around him, he would have to rise to their level, a feat I could see him being very capable of. Perhaps the secrets of his own people's past were revealed to him as well.
If he hadn't done this, I could see his life Tol Eressëa becoming more of a burden then a pleasure, and Frodo becoming a figure of pity, rather than admiration. And I would sincerely hope that he would gain the privilege of being allowed into Valinor, as well. By the time Sam arrived on the Lonely Isle, I wonder if the Frodo he met there would even bear any resemblance to the Frodo that left 60 years before.
As to Rosie's small role; I don't think she contributed to Frodo's illness. She and Sam seem to be the only connection he still had to the people of the Shire. And Tolkien did indicate that he enjoyed their company, (as well as enjoying the benefits of having the Gamgees there to run the household, while he worked on his writing.)
I would not like to read that Frodo had to suffer through all his "flashbacks" alone. That would be far too sad. Sam and Rosie did the best they could for Frodo, it was just, unfortunately, not enough.
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