^TNG's "Tin Man" isn't really the best example there, since it's an adaptation of a 1979 novel which is in turn an expansion of a 1976 story. So its living ship predates any of the other examples you list.
And how can you guys be citing TNG and B5 as examples of "bioships" and ignore Moya from Farscape?
Well I don't think any of us were trying to be comprehensive...as I mentioned the first
story with a biosip was likely in 1953, there was at least another in 1967, and Doctor Who had the Axos and Zygons in the early 1970s.
I can't stand Farscape so I try not to mention it as much as possible, but Moya was pretty cool.