I doubt Lady Macbeth is writing anything coherent in her letter. She is probably scribbling, or repeating something about spots. Her own words are completely incoherent babble. She is unaware of everything around her. She is saying things like this:
The Thane of Fife had a wife; where is she
now? What, will these hands ne'er be clean? No more o’
that, my lord, no more o’ that. You mar all with this(40)
starting. (Act 5, Scene 1, enotes pdf p. 77)
She sounds like a woman who has lost her grasp with reality. Chances are you wouldn’t find the letter. The doctor and gentlewoman are quite cautious about making sure they don’t get caught hearing anything that Lady Macbeth has been confessing to. They know it would mean death for them if they did. They pretend they know nothing, and would likely destroy the letter. I think that if you found the letter, you would not be able to read it anyway. I doubt she can write at this point.
Keep in mind, too, that Lady Macbeth found out about the witches' prophecies through a letter from her husband. It was immediately after she read this letter in Act 1, sc. 5, that she hatched the plot to kill Duncan. Possibly the letter that she writes has something to do with the letter she received from her husband or it was Shakespeare's way of bringing the story around full circle since her letter writing comes shortly before her own death.
According to the summary of Act V scene 1 in eNotes:
The Gentlewoman reports to the Doctor that Lady Macbeth is sleepwalking and her behavior is very strange. The Gentlewoman says that Lady Macbeth gets out of bed, puts on a nightgown, unlocks her closet, writes on a piece of paper, seals the letter and returns to bed.
It is unknown what Lady Macbeth writes when she sleepwalks. All of your suggestions are excellent ones. I would tend to believe that since she is walking and confessing in her sleep and the gentlewoman says Lady Macbeth has spoken things she can not repeat, that Lady Macbeth is also writing the confession down. She raves about the blood on her hands and mentions the deaths of Banquo, Lady Macduff and her family, and Duncan. All of this is probably in writing as well in order to relieve Lady Macbeth of her guilt. When the relief she seeks does not come, she resorts to suicide.