I don't think the problem is with "seems to have been", it's more with usage of the present perfect iteslf.
1A) That man seems to have been rich before.
(1B) That man seems to have been rich in those days.
I would never say "He has been rich before" or " He has been rich in those days" in the first place. I would say "He used to be rich", "He was rich" or "He was rich in those days"
(2) Ken seems to have been interested in Japanese History.
Again, "Ken has been interested in Japanese History" doesn't really make sense by itself. You would need a for/since to complete it.
(3) Tom seems to have been learning Japanese for a long time.
This one would be fine, being completed by "for a long time"
(4) His English is perfect. He seems to have been in the United States for a long time.
Again fine. Makes sense, with a context, and completed by "for a long time"
(5) She seems to have known the truth.
An odd sentence. You would need "for a long time" or similar to complete it.