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 one 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.