After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang IT from.

In the above sentence, IT cannot logically refer to fire, yet the meaning is ambiguous.

As long as both the nouns "deer" and "fire" can be followed by the pronoun IT since both make grammatical sense with it, what sounds like the simplest solution here is to repeat the noun "deer" to clear any ambiguity.

And so:

After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang the deer from.

After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang IT from.

In the example above, IT cannot logically refer to fire, yet the sentence is ambiguous.

As long as both the nouns "deer" and "fire" can be followed by the pronoun IT since both make grammatical sense with it, what sounds like the simplest solution here is to repeat the noun "deer" to clear any ambiguity.

And so:

After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang the deer from.

As long as both the nouns "deer" and "fire" can be followed by the pronoun IT since both make grammatical sense with it, how about simply repeating the noun "deer" a second time to clear any ambiguity?

After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang the deer from.

After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang IT from.

In the above sentence, IT cannot logically refer to fire, yet the meaning is ambiguous.

As long as both the nouns "deer" and "fire" can be followed by the pronoun IT since both make grammatical sense with it, what sounds like the simplest solution here is to repeat the noun "deer" to clear any ambiguity.

And so:

After roasting the deer, the hunter extinguished the fire and then searched for a tree to hang the deer from.