First, `fuŝ-` is a (verbal) radix, stem word. The usage above is perfectly fine, where English would use two separate words.

- kantaĉi = sing ugly (la rano/knabineto kantaĉis = the frog/little girl sang dreadful)
- fuŝkanti = sing with wrong technique/mastery (like drunk)
- fuŝkantaĉi = both

Here it is a difference in nuance.

Your aim would be something like:
- malbelkantaĉi = ***

Which is an ugly word creation itself.

To strengthen `aĉ` on may use:

- kantaĉegi = sing very dreadfully
- tre aĉe kanti

By the way `kantaĉi` one would not translate natively with `sing`+adverb,
but more something like `whine`, `belt out`, `yodel` (?). But I am not native.