] I get the feeling they are trying to put the idea of marriage into her head. I can't point to any evidence to support this, but I will go over the play again and try to explain my view clearly.

Queen Gertrude certainly had it in mind. At Ophelia's burial, she scatters flowers and says something to the effect of, "I hoped thou would have been my Hamlet's wife" and "I thought thy bride bed to have decked, sweet maid/And not have strewn thy grave." So the idea does exist.

That's why I really get furious with Polonius when he warns her away from Hamlet. Maybe he's just trying to be clever and protective, cynically assuming that Hamlet must marry elsewhere and so could not offer marriage to Ophelia, but Gertrude certainly has no objections. Whether there would have been any from Hamlet Senior if he had lived, or from King Claudius, I don't know, but at least Hamlet's mother would have favoured it.