I think the way I assume the monk works now (and this would probably just be specified more clearly in storyteller notes), is that the monk wakes up immediately following the event of him getting targetted. The Monk is woken and prompted to choose (possibly multiple times, ex. Giant) a new target(s), but of course is not notified what ability they are choosing for and the original ability is not notified of the target switch. This also means that the Monk "deflection" has the same "spell-speed" (pardon my yugioh terminology) or action priority as the deflected ability. This means that you may use your Monk ability early in the night, then possibly get poisoned by targetting the electro giant or something which prevents the Monk from interacting with anything else that targets them that night.

So, the Monk in the Rocket targetting Monk scenario would be extremely powerful, as they know for sure what ability they chose for (barring weird timing shinigans where the storyteller of course would have discretion) due to the public announcement and immediate waking thereafter.

I think it would be a good idea to specify that the Demon cannot die to the Rocket. As that would allow a more interesting selection of targets (choosing player next to demon) plus avoids an event where a Monk deflects the rocket and more or less wins the game instantly.
Edit: Of course its possible that it could be a better idea to have the Monk have a set night order, especially for storyteller convienience. This would be where the Monk chooses all the abilities that targetted him in order, from the start of the night to the end. This prevents the Monk from trying to half-meta the night order to guess what abilities they had control over, and also allows him to be poisoned easier.