Well, my first suggestion is to instead of using easy way, less easy, tricky, hard, ect, is to steal from 4th DnD's skill challenge options as they are very similar. Require X successes, but Y of them need to be this skill and you can only use Z skill once. Everything else can set up aspects but not count as success.
There is also the Rodrigo method, from Critical Hits. His homebrew is that you cannot roll the skill you rolled last turn and you cannot use the one the player before you just used. I've used the successfully in multiple systems, including Dresden. Here's a more detailed explanation and an example from the podcast starts around 24:30 and goes till 39:00 but the wrap up is a little longer. Some background in case you skip right there, it's a D&D adventure, party almost wiped last session in a tower fighting skeletons. The wizard alone survived by retreating and has come back in to try and rescue his friends.
To give a personal example, I ran a Dresden game where the players needed to get from New York to...I believe it was a white council meeting? Not sure. Anyway they had to do it fast and since they had a wizard they thought planes would be a bad idea. They went through the never never and ended up in a Fae mapping of the Labyrinth, from Greek legend. Instead of drawing a maze, I ran it as a skills challenge. They needed to get, I think it was 5 successes, before 3 failures. I narrated the area of the labyrinth they were in, a hedge maze, looked familiar, to the point they were sure they were there before. They were stuck in an endless loop. Wizard rolled evocation to burn through the hedges and they exited to a new area, where there was a giant venus fly trap. Werewolf distracted it with agility, nipping at the plant, while everyone got by. They then came across a set of statues, and the champion of Odin tried to figure out what they were using lore. He failed and they grabbed him. I forget the next two failures but they ended up getting stuck and the winter knight appeared with the Minotaur to slaughter them. In order to survive they jumped out of the never never without looking, ending up in the Hudson bay I think.
Using this method it kept people engaged and the requirement to switch skills demands that people don't always default to their best, keeping things varied and interesting. As you can see, the basic mechanic, roll X success before Y failures is the same. The idea of approaching things the wrong way still applies. Trying to use fire on the hedges was easy, however trying to know about a random set of statues in an old and mythical place was very hard. The labrynthin is meant to be mysterious and unknowable, so lore was always going to be difficult, similar to the hard vs easy approaches. It's quick and simple because you don't need to map anything out. Just set the outline of the challenge and react to the players ideas. The only place it becomes more complex is that skills are more specific than approaches and as such isn't quite as elegant though slightly more elegant than the base Skill Challenge from 4th. Though I suggest reading up on advice for those anyway. You may find that specificity of some examples actually maps better for certain scenes than the vaguery of a cliffhanger.
To maintain that elegance both example loss quickly, you should use just use Modes as your categories. Modes perform a very similar task to approaches, in grouping skill actions into a larger more inclusive category. However this still doesn't seem great as some Modes don't map well to the "how" style of approaches. So instead of modifying Cliffhangers, why not modify your character sheets to include approaches per the conversion guide?
