It depends if any of those were 'personal gifts'. The ones that were given on a tour, may have been Diana's for her use, but they would belong to state. We don't know which of those jewels you mention may actually be Diana's. It also takes quite a bit of money to rework a tiara.
Harry is not personally rich. Unless he wants to lose his income. It is more likely if she gets a new tiara, will be a gift from the queen or Charles.
Not sure she will get new. There will be question if she is really accepted if no family piece. Besides the BRF knows all too well, that tiaras in junior branches often get lost. In a generation or two, the tiara wont be needed, and may be sold off for inheritance taxes as many have. Harry's children, and grandchildren quite likely, will likely be loaned a tiara from Grandpa Charles, Uncle William or cousin George when or if needed.