What you posit is reasonable except for one thing: The Deck of Many Things has a random outcome that the DM determines by a die roll.
As a magical artifact, I would say that it consists, as a whole of the cards it contains, not of a bunch of independent magical cards. The whole Deck itself is the magic item here, not the cards themselves, they are just pieces/components of the larger artifact. So the individual cards do not necessarily have an independent existence outside of the deck, nor any independent, fixed or specific order inside of it. When a character draws a card it is "randomly" determined by the Deck.
And this element of randomness is very important to the artifacts nature and being (in fact I would say that it is the central attribute of it). So, technically, the DM should re-roll the die if the draw/turn gets re-set, not just play it as though there now (or ever was) any specific pre-determined card on the top of the deck. (of course that's up to the DM).
Look at it this way: If a party engaged in combat resets the turn with Forced Dream, is the DM going to say that the turn gets played over, but everybody get's exactly the same attack and damage rolls as the first time? Or does the DM rule that everything has to be re-rolled fresh and as it happens? My guess is most DMs would say the second, both for combat and for the Deck. Which means that while Forced Dream could be used to avoid a bad outcome from the Deck, it could not be used to then force that same bad outcome on someone or something else: it gets a new random roll.
You should only get as many cards as you declare - three
The character being removed from the deck's presence opens up some some cause and effect chains, but it is the two remaining cards (not yet drawn) that erupt after the hour, not "the whole deck unleashes at once" as stated in the question's text.
Three cards should get drawn, but the last two may not be usable
If you fail to draw the chosen number, the remaining number of cards
fly from the deck on their own and take effect all at once.
If you declare three, and you only draw one, then after an hour the other two cards come out of the deck and take effect immediately. The text does not specifically state "the whole deck," so this reading of that description makes the most sense to me.
That doesn't completely solve the conundrum. The DM will need to make a ruling on which card takes effect first, but the description suggests that you aren't drawing the cards at this point: they are being drawn for you by the magic of the deck. Let's call that "autodraw."
The above 'draw no more cards' lacks a card drawing character, but it leads to some other "how does this work?" questions for the DM to resolve.
Example based on your scenario:
First card: Jester (yay, XP for you)
Fail to draw, so one hour later ...
Second Card (autodraw): Donjon (you are trapped!)
Third Card (autodraw): The Fates (you can undo Donjon1, lucky you)
or
Third Card: Balance (you are trapped and you change alignment).
or
Third Card: Knight (The DM may rule that he appears wherever you are trapped, so maybe he can help you get out1, but he may appear where the deck is and where you are not).
1 What suspended animation means, for this result, isn't explicitly spelled out
Donjon. You disappear and become entombed in a state of suspended
animation in an extra-dimensional sphere.
We can get an idea from the Astral Projection spell description (PHB, p. 215):
... the material body you leave behind is unconscious and in a state of
suspended animation; it doesn’t need food or air and doesn’t age.
The Sequester spell description (PHB, p. 74) says for suspended animation ...
"Time ceases to flow for it{what's being protected by the spell} and it doesn't grow older."
It appears that you'd be awake, and maybe able to communicate with that Knight, but the DM may rule otherwise. (For example, the DM may rule that the Knight pops into existence where you are as you pop into that other place).
Which spell description's sense applies? DM ruling needed here.
Best Answer
You Might Only Be Able to Declare Once
With no duration described for this or similar limitation, there would be no effect created when drawing additional cards beyond what you've declared. Even if you announce some new number at a later point, those draws would be in excess of the originally declared number.
This interpretation is fairly broad as a limitation of the deck for what's written here, but it's consistent with previous edition's versions of the item which were more explicit.