It's a bit controversal question. Some grammarians say that the present perfect continuous tense doesn't exist in the passive form. They say that the nearest equivalent of a sentence such as They have been repairing the road would normally be The road has been repaired lately. They have been constructing the building for four months would be The building has been under construction for four months.
Others say that sentences in all tenses can be formed in the passive forms; the present perfect continuous is no exception. However, its use that is less common should be avoided. According to them, it should be used to express events recently occurred in the past and continue in the present. For example, The toys have been being broken by children. Too much pollution has been being dumped in the river.
In light of the above, I would go for the sentences presented by TRomano in his comments. Alternatively, you can start your sentence with "being" or "having been"
as suggested in the question.