I have the One Ring in play and 2 Hp. There are 3 Burden Counters on the Ring. I click to put a stop on my Upkeep to be able to play Instants or Tap the One Ring while it is on the Stack to draw more cards. At my Upkeep, the stop is removed, goes strait to damage and doesn't let me press the key to go in Full Control Mode, losing the game instantly.
In MTG you are able to interact with your Upkeep and this is just not how the rules are supposed to play out.