Hi sls
.
You intuition is leading you in the wrong direction.
.
Generally speaking you would have this word order:
[color=blue]modal verb + not + have + past participle
might not have done
may not have done
cannot have done (can’t have done)
could not have done (couldn’t have done)
will not have done (won’t have done)
would not have done (wouldn’t have done)
should not have done (shouldn’t have done)
ought not to have done
must not have done
You might possibly hear the word not after the word have from time to time, but that wouldn’t be the “normal” word order (and would probably only be done for some special reason – such as extra emphasis on the word not).
By the way, in spoken English you’ll usually hear a double contraction with many of the above forms: