No. "Overkill with the locks" is not possible.

I carry three "U" locks, Four Cable locks (5; 6; and 12 foot. Only the 6 foot has an integrated lock) and one 3 foot chain lock with integrated key lock.
They are carried either in or on a basket, or in my trailer.

If some low life is going to steal my bike or trike, the S.O.B. is going to have to work to get it.