And why might (1) have been preferable to (3)?
In spoken language, in commercial documents or in literature?
As a native speaker I can tell you that sentences like this are only used in literature. In literature however artists are often use their own style which differs a bit from "official" grammar.
(1) Um so viel zu riskieren, muss sie mehr als nur einen Verdacht gehabt haben.
(2) Um so viel zu riskieren, hat sie mehr als nur einen Verdacht haben müssen.
I doubt that most Germans would unterstand the difference between the two sentences and I even doubt that I do!
In other words: Most Germans (including me) would only hardly understand the difference between the two sentences and if they were in the situation that they had to write a book they would use the wrong variant with a 50:50 chance.
I tried to simplify the two sentences and I ended with this:
(1) Sie muss eingekauft haben.
(2) Sie hat einkaufen müssen.
In the first example the word "müssen" is in the present while the word "einkaufen" is in the past.
Just like in English the word "must" or "müssen" can have two meanings in German:
- "She" is (now) in some situation where it is neccessary that "she" has already been shopping / has already finished shopping ("eingekauft haben" is in the past!)
- We have (now) evidence that "she" has been shopping (in the past). (I think your example "(1)" is exactly meant like this.)
In the second example however the word "müssen" is in the past while the word "einkaufen" is in the same time as the word "müssen". Therefore the sentence may have the following meanings:
- "She" was (in the past) in a situation where it was neccessary that she goes shopping.
- We had (in the past) some evidence that "she" is (still) being shopping. (I doubt that this meaning is used very often.)