You've asked a good question, Leith. I can see why you're asking this, and I can also see why the two native speakers who responded both said it was incorrect.
Here's the thing: In theory, it is actually correct: there is no grammatical/structural reason why you can't say "The room has been being cleaned". However, in reality, this structure does not exist. As you pointed out in your comment below '.....the present perfect continuous cannot be changed into passive voice'. This is because it's just too complex and cumbersome to use.
If you want to refer to the result, you could, of course, use the simple aspect and say 'The room has been cleaned'. This is a present perfect passive ( not 'past tense', as I'm sure you know).
However, if you really wanted to focus on the activity by using a present perfect continuous, you'd find some way to avoid the passive. A typical workaround would be 'They've been cleaning the room'. The vague and impersonal 'they' avoids mentioning who has been doing the cleaning and also sidesteps the awkward passive construction.
I hope that helps.