I'm with Edinburgher on this and struggled with the Susie example too. Mustn't have can work as an epistemic modal (supposition) but not as a deonic modal (obligation).
I certainly thought this initially, Natkretep, but it occurs to me that there are occasions in which the formula can have deontic (obligation) use.
I'm clear that the answer to the question in the OP, Can "You mustn't have done that" have a similar meaning to "You shouldn't have done that" / "You were not supposed to do it (but you did)"? (not logical probability but obligation),
is No. We all seem to be agreed on that.
However, where we are talking in the present about things which are required (obliged) to have happened in the past, we can use it in a deontic sense, it seems to me.
The BNC, the British Corpus, bears me out. Here are some examples to illustrate the point I'm making:
The client must not have previously been refused representation
- The modern English legal system. Gunn, N J and Bailey, S H. London: Sweet & Maxwell Ltd, 1993.
Entrants must be aged 16 to 25, and must not have done any professional modelling or have an existing portfolio
- The Sunday People
In June 1989 the government refused to grant the fundamentalist Islamic Nahdah movement (Mouvement de la renaissance) legal recognition as a political party, on the grounds that by law founders and leaders of parties must not have been convicted of offences warranting more than three months' imprisonment or six months' suspended sentence; 15 Nahdah leaders, although at liberty, still had current convictions dating from September 1987 (see p. 36633).
Keesings Contemporary Archives. Harlow: Longman Group UK Ltd, 1990,
(1) The Consultant you have chosen must not have been involved in our client's treatment. -
Know-how for personal injury lawyers. Walker, Ian. Harlow: Longman Group UK Ltd, 1993.
Just in case this was exclusively a BE usage, I checked the COCA, the AE Corpus, and found several examples, for instance:
Previously, that power rested with the California Legislature. Members of the commission must not have run for state or federal office for the previous 10 years, been lobbyists or donated more than $2,000 to any one political candidate.
Dueling propositions on legislative borders; Campaign 2010 San Francisco Chronicle
They can't get married in the Church of England, the Anglican Church, the official church of the country Prince Charles will one day reign over as king, because as defender of the faith, he must not have divorced.
My Word, Fox_Gibson, 2005.
I'm not at all saying that the must not have + past participle
formula is exclusively deontic (obligation) - epistemic (supposition) examples are much more common. The example in the OP must be supposition, in my view, but there are certain cases, such as I've tried to illustrate, where a deontic meaning is idiomatic.