The word "most uncareful" can be interpreted in two ways: either as someone who is extremely careless, or as someone who is extremely careful. To find the antonyms for both meanings, we have to look at opposite words that convey the opposite meanings of the two interpretations.
For the first interpretation, antonyms for "most uncareful" could be "extremely careful", "meticulous", "conscientious", "attentive", "vigilant", "diligent", or "scrupulous". On the other hand, for the second interpretation, antonyms for "most uncareful" could be "extremely careless", "negligent", "reckless", "heedless", "inattentive", "thoughtless", "rash", or "irresponsible".