Present (and recent) time:
a. He must be asleep [already].
b. He must be sleeping [already].
c. [I think that] he must have [already] gone/went to sleep/bed.
d. He must have been sleeping for the last eighteen hours [before now], if he has not heard that.
However, I will contend that c and d in the above are rare, and that "must have" is much more commonly related to past events.
a. By that time, he must have [already] gone/went to sleep/bed.
b. By that time, he must have [already] been sleeping.
c. He must have been sleeping for the last eighteen hours [before that time (in the past)], if he had not heard that.
Thus, the problem with the verbs in 1 and 2 is that they're usually made for past time, while the application required something appropriate for present time.
And the modal + "have/perfect infinitives" makes for a difference: when using "have/perfect infinitives" you are not getting the connection with the present that is created by the present perfect. With the modal + "have," you're describing events that are mainly in past time.
Modality and the English Modals By F.R. Palmer
The modal verbs are not normally used, therefore, in past tense forms
to refer to past judgments. Past tense forms are normally tentative
with present time reference. It is, of course, possible to report past
judgments, but this requires verbs such as THINK. BELIEVE, etc.
In contrast, the proposition can be in the past, for we can make
judgments about past events. This is achieved by the use of have
before the main verb:
Well, he must have been flying too low. (W.5.3.n6)
Davidsen-nielsen:tense and Mood in Engl. Tiel 1: - Page 167
Niels Davidsen-Nielsen - 1990
'I must have been in the garden when you called.'
By using the present perfect in examples like these the speaker
informs the addressee that on the basis of present time evidence it
is his conclusion that a certain event has taken place.
The New Cambridge English Course 3 Teacher's Book By Michael
Swan, Catherine Walter, Desmond O'Sullivan
Modals with perfect infinitives: You may need to remind students that most
modal verbs (e.g. should, must, may, might) do not have normal
past forms. However, a special structure is possible in which the
modal verb is followed by a perfect infinitive (should have gone,
might have been). These forms are used to talk about events and
situations (usually past) which did not take place or which are not
known for certain to have happened.
This reference further shows that "must have" is mainly used in past time in both AmE and BrE:
American and British English Preferences: Spelling, Grammar, Punctuation ...
By Nancy Salama, Mary Ghali
The Mirror of Parliament for the ... Session of the ... ... John Henry
Barrow - 1834
Mr. O'CONNELL.— Honourable Gentlemen must have been sleeping for
the last eighteen years, if they have not heard that.
- And why can't He must have been sleeping describe the present? It is the present perfect tense, after all.
No, it's not the present perfect in all cases. It's mainly a modal form that is related to the past.
Now, one could reply on the phone:
Sorry to answer only now. I must have been sleeping at my desk.
and then it has a present perfective meaning.
But in general see this ESL teaching expert and moderator here:
Must + present perfect (which is one of the modal perfects) means that
the speaker or writer is sure that something happened or didn't happen
in the past.