So I started wondering, could you play IDFT under FATE?
I think you more-or-less can.
Characters have a high concept and four Aspects. It’s a good idea to make sure that, overall, they offer both advantages and weaknesses for your character so you can regain FATE points.
Characters begin with four FATE points.
You don’t need any skills, although you can still use them; a small number may help define characters mechanically and will change the difficulty of the game. Most skill rolls are assumed to have a difficulty of 0. Easy tasks have a negative difficulty. Similarly, there's probably no reason to include stunts.
There are four Stress tracks: Stamina, Nerve, Luck and Time. Each has ten stress boxes. Stamina and Nerve also have 2-point, 4-point and 6-point consequences.
Whenever a situation is physically exhausting, unnerving, time-consuming* or a matter of chance, roll the Fudge dice and apply any appropriate consequences or Aspects. If the result is negative, apply it as Stress to the appropriate track. Otherwise, the number represents one Tick’s progress towards the difficulty of the task set by the GM.
*Exception: the Time pool is never rolled during confrontations, when other pools are used instead.
A PC may make skill rolls to accomplish various things, including as a supplement to a Stress roll. It is up to the group to determine the mechanics of the outcome. For example, a character may attempt to scramble over a wall when using Stamina to flee a monster. This skill roll takes no additional time, and a success will create an advantage that assists with the Stamina roll. In another situation, succeeding (or failing) at the roll might change the narrative sufficiently that it makes no sense to continue with the current set of Stress rolls.
When the PC is resting, they can regain one Stress box in each of Stamina, Nerve and Luck. However, this consumes one Tick of time and requires a Time roll.
Consequences, as usually, cannot be healed directly. It is possible to mitigate the effects of certain consequences by taking suitable actions (locating and using medical kits, resting, finding crutches, staunching blood flow and so on) and making skill rolls.
Many tasks, such as searching a room, reading a book, repairing something or having an argument, may call for both skill rolls and a Time roll. Sometimes Time is consumed simply by delay, when a character waits.
When the Time pool is exhausted, problems arise again and the characters must move on or confront them.
The lighting properties of both rooms and light sources are modelled using Aspects. Any light source has a Fuel stress track, and a stress roll is made when the GM deems it appropriate. Of course, Aspects may help with this roll.
Did I miss anything? I don't think it's as thorough, but it's meant to be a workable hack rather than a full game.