Cryptex Hunt 2022/Test your babysitting skills in this realistic scenario

Test your babysitting skills in this realistic scenario is an interactive puzzle and the seventh puzzle of the 2022 Cryptex Hunt. It's presented as a game similar to the many fake sliding-rod puzzles that get advertised in free apps.

Solve Paths
The puzzle itself is fairly straightforward, and just requires some trial and error to figure out the correct order to pull the rods, particularly knowing that all five need to be pulled eventually. In order to properly finish the game, take the following steps: Reading the letters of the rods pulled in order will get solvers their answer.
 * Pull E. Nothing will happen.
 * Pull A. The robber will enter the house and take the easy exit via the back window, bringing the safe with him.
 * Pull R. With the safe gone, the bathtub will fall, but the cake will stay intact.
 * Pull L. The tub will block the cold air, which will freeze the water inside it.
 * Pull Y. The girl will be able to reach the cake (and without having to take a bath!).

Part 1 Final Answer:

During the trial-and-error of trying to finish the game, solvers may discover one of the game's five "Game Over" states, each with some highlighted text and a rating of 1 to 5 stars. Additionally, they may take note of the url of the page the game is on (gorey.games), and the text received upon successfully completing the game (Enjoy the cake! Mind the tiny crumbs). The words "tiny" "crumbs" and "gorey" should lead solvers to Edward Gorey's "Gashlycrumb Tinies", an alphabet book documented here (among other places). Each game over's highlighted text references one of the entries in the book, as follows: Reading the first letters of the children's names in order of the star ratings for each game over will get solvers their answer.
 * Loved cake, hated baths, perished of hissy fits. --> Susan (Pull E, A, R, Y)
 * Embedded in ice. --> Winnie (Pull L)
 * Fell down the stairs. --> Amy (Pull Y)
 * The cake flew into bits. --> Titus (Pull R)
 * Done in by a thug. --> Hector (Pull A)

Part 2 Final Answer: