What evidence do you have that the use of the word "kind" in Genesis was meant to establish an immutable divine taxonomy? I believe that the more usual interpretation is that it is intended to express the orderliness of nature--figs don't grow on apple trees, cows do not give birth to sheep, that kind of thing. In a sense it is an expression of the Darwinian Principle of Reproductive Similarity.
I agree with your reproductive similarity idea it is the essence of Christ's sowing and reaping principle...if you plant tomatoes you get tomatoes...tomatoes never produce cucumbers.
Biogenesis states
a. all life comes from life
b. all living things arise from their parental host
In the Bible what we see is that after God created (having already built into creation the laws of physics and chemistry to govern the matter/energy He had made), He used the materials of the earth (elements, molecules etc.) to make the form or material part of creatures but life (bios) came as a result of an act on His behalf.
So in one sense it can be seen as life arising from non-life but what it describes is biogenesis (God is the Life in the Universe) He makes these material forms live...non-living matter has no power of its own to live (animate, respirate, eliminate, reproduce, and so on).
Now then as to the Biblical "kind", the ancient Hebrew "miyn" from the root "to sort" or "to portion" according to Gesenius Heb-Chald lexicon defines the word as "species, kind, sort" and rreelates to a cognate root in Syriac meaning also f that you amily or race.
The Greek "genos" later called genus by some is actually an aggregate term meaning collectively type, offspring, kindred, etc. (or to diversity in said classifications) and is used to describe descent from a particular stock.
So we can see the Bible (not that you accept that) describes different categories...man, beasts, fish, insects, birds, etc., or example read 1 Corinthians 15:39