Difference in meaning: "would have had to be" vs "would have had to have been"
Solution 1:
"He would have had to have been there" means that, in order for him to have accomplished whatever he accomplished, it would have been necessary for him both to be there and then to leave. In other words, whatever he was supposed to have done could not have been accomplished only by him being there.
Most commonly, however, the action done at the place is simply done at the place, and leaving the place is not required to perform the action. Therefore, we usually say something like, "For him to do what he did, he would have had to BE at that place," because merely being there is adequate to the task. Leaving the place has nothing to do with what he did while he was there.
A quick example: "For Watson to have murdered Lestrade, he would have had to be at Lestrade's apartment." This says it was necessary for Watson to be at Lestrade's apartment (given that the murder occurred in the apartment), but accomplishing the murder did not in some way require Watson BOTH to be there AND to leave.
Now, "have been there" is also logically quite possible. Let's say Sherlock determines that although Lestrade was murdered in Piccadilly Circus, the murderer couldn't have done it unless he had previously been at Lestrade's apartment to see Lestrade's calendar and thereby to know when Lestrade would be found at Piccadilly. In which case, for Watson to have murdered Lestrade, he would have had to have been at Lestrade's apartment beforehand; in other words, Watson would have had to be at Lestrade's apartment and also to leave the apartment (to go to Piccadilly to commit the murder).
Now, all this having been said, we don't usually construct the sentence as elaborately as in the first example ("would have had to have been"). It is not necessary to put the main verb into the conditional present perfect ("would have had"). We usually say simply, "would have to have been."
Solution 2:
These sentences do have different meanings though the second one is less likely given the absence of a specific context.
(1) He would have had to have been there [(in order) to have done something].
John, the choice of tense does NOT imply that he can't still be there, although you wouldn't say this if you and your interlocutor both knew that he was still there. The implication is that you didn't know that he had gone there, but now you have evidence that implies that he was there at some point (and indeed may still be there - perhaps you are detectives trying to find him).
(2) He would have had to be there [(in order) to do something].
This sentence sounds stilted out of context and would be quite rare. B Geek gives some examples of the kind of context that would enable this. For example it creates immediacy, by removing a layer of pastness: we've just got off the phone and then are wondering where he was calling from - could he already be in Tel Aviv?
[Before he could leave]: He would have to be there [since he couldn't ring from anywhere else]
[He has probably left but]: He would have had to be there [at the time of the phonecall]
[He has passed that point so]: He would have had to have been there [at some unspecified point]
Note that I have emphasised occurences of hafta or hadta that have the sense of must. This is a complicating factor in this sentence. These are marked by tone, stress and devoicing and don't sound exactly the same as the possessive or auxiliary have/had:
A list of things I have to do during my holidays.
Devoiced reading 1 (must: e.g. work will never let go of me even when I am on holidays...)
Devoiced reading 2 (must: e.g. a list of the places I want to go and see before I die...)
Voiced reading (possess: always bored during the holidays but gran gave me this great list...)
Solution 3:
"He would have had to have been there." - This is what you would say if, for example, you were telling about something funny that happened to you earlier and someone listening didn't find it funny- "He would have had to have been there; it's really not as funny without the image of what his face looked like..."
"He would have had to be there." - It is my opinion that this is confusing because it is simply incorrect- you cannot go mixing past and present like that. Either "He has to be there." or "He had to be there." Either "He would be there." or "He would have been there." Either "He would have had to have been there." or "He will have had to have been there."
The proper way to write what I think you mean to say with "He would have had to be there." would be "He would have had to HAVE BEEN there." I imagine that the "have" is left out sometimes in every day usage out of laziness but if "been" is "be" it's not right.
As always, what I am saying is my understanding of the language and could quite possibly be directly at odds with what the rules say, so please correct me if I am wrong.