I have some ideas for the game if you would like to hear them:
1. In the room with a large clock, near Bowser's final level, you must solve a clockwise puzzle, but if you fail, the clock will chime, alerting Peach ghost.
2. In the infinite stairs area, it could be the same, if you don't get all the trophies, the stairs will be endless, and they could also make noise to alert Peach ghost, and where are the Peach paintings on the stairs, when these are endless, that they see the photo of Peach ghost.
3. In the area of the second level, where there is water and the entrances to the levels of fire and desert, there is an area with water, there could be a hidden ghost eel, which will stalk you, you notice it because the water will move where this is and you must get out of the water before it catches you.
4. I have an idea for the third level area, the corridor where the pictures of the water and mushroom levels are, where the doors to the large and small levels are, and the room with the mirrors. There could be ghosts of Toads, who haunt you like the Boos, and like the weeping angels of Doctor Who: that is, they follow you if you turn your back on them, but if you see them they stay put.
5. Why does Mario go to the castle? Maybe someone sent him a letter of help, it could be Toadsworth or Luigi, the princess has him trapped somewhere and if you collect all the statues you will free him and Peach ghost will rest in peace, and if it is Luigi who you rescue, he could appear at the fountain in the backyard, where the statue that says "L is real" is.
6. I have a theory that Mario couldn't save Peach after she was kidnapped and that's why she died, and that's why he hunts Mario: for revenge. So you could face her after getting all the statues in the same battlefield where you face Bowser for the last time, with a star shape, and while being chased he must collect star pieces that will hit Peach, and repeat that 3 times until that her soul is appeased, she forgives Mario, and the soul of the princess finally rests in peace.
7. The last idea is that there could be power-ups, some mushrooms, that keep Mario's stamina full for just a few seconds.