I know that I cannot say like this:
I would love to be living in the 19th century
because this is not a real oppotunity and you can't live in the past. I spoke with my American friend and he suggested this variant:
I would love to have been living in the 19th century
But I don't understand why it is correct. I think that saying "have been living" implies that action have been lasting for some period and finished recently or still continues. But it cannot be with the 19th century because it wasn't recently, it was more than 100 years ago.
Is there any rule or grammar which could clarify the present perfect continuous tense usage in this sentence?