If humans evolve from mindless, thoughtless entities which do in fact seek quality, ought not we to apply a soul to any form of matter, living or not?

Your question answered itself
you asked saying that that things seek quality
you stated that as a fact
the concept of seeking implies purpose
therefore you have answered your own question
entities seeking purpose arrive at answers

So....do you think a rock has a soul? If you do, it means that the whole planet is some kind of life form and you are probably an Earth worshiper who puts the planet first, then animals, then plants and finally mankind at the bottom.
In that mind set, man is little better than a parasite and the question of his soul becomes mute as all other souls are above his.

If you are asking if humans are the only species that has a soul, you are not Christian and there for the question is mute because only Christ and God can answer the question.

yes, humans are the only beings that have souls. We are the caretakers of this world and all the life on it which was created for us by God and He knew it to be good. It is sinful to willfully abuse this planet or the life on it. We should all keep in mind that our world and the life on it was given to us by our Creator not to be abused and wasted but to be used to better our lives and our Selves. Serve God by serving man, there is no higher calling and thus the answer to who has a soul. We do. not rocks, trees or dogs...just us...all the rest is FOR us. We were not put here for their benefit, they were put here for ours.