So 'I diswant ice cream' is a stronger statement than 'I do not want ice cream', though most people, whose language is less considered and precise, would (also) use the latter to cover the former.

Minor point of information. In English "do not want" is not the negation of want. It actually means what you have defined "diswant" to mean. The "not" is privative here, not merely negative. People are not being less considered and precise when they use it this way. They are using the words precisely as everyone but you uses them -- that is, precisely in accordance with what they mean.

You are welcome to invent a new language, just like English except that "not" always means simple negation and never means privation; but that language is not English. Neither, for that matter, would the corresponding modification of French be French. Comparing the morphology of translations of "want", "do not want", "have", and "do not have" in a further selection of languages with Google Translate suggests that the range of languages for which this is the case is large.