I still have yet to study the Rav Chaim Soloveitchik essay on the subject of keeping Sabbath and work done not for its own sake. However, a few day ago I wrote my own answer on the issue of the contradiction in the Rambam/Maimonides.
Yesterday [on Shavuot] I opened up the Reb Chaim (Chidushei HaRambam) without my learning partner and I noticed that the major issue he deals with is not the contradiction in the Rambam but the fact that the Talmud in Keritut does attribute the argument about stirring coals to the idea of it being a thing that is not intended.] So first of all even if my answer is correct it does not in any way relate to the major problem Reb Chaim is dealing with. and just off the top of my head without looking at it in depth it seems to me he is trying to say that it is as the Gemara itself says a thing not intended and he understands that the argument there depends on the Aruch [a rishon/first authority quoted by Tosphot]-- that a thing not intended but a pesik reisha (the work must happen in spite of the fact that he does not do it directly) is forbidden to Rabbi Yehuda because the pesik reisha bring the intention to the thing and to Rabbi Shimon it does not.
If in fact this is what Reb Chaim means, then everything is fine. And as for the contradiction in the Rambam I am not sure of how he explains it. But my idea I think is true. If you just look at the Mishna, you will see that it seems to be saying that capturing any reptiles besides the main eight, if done not for the sake of keeping them is not a work on Shabat at all. Not that it is a work done not for its own sake.
And I did not mention it, but as for chabura [wound] for the other thing the Rambam allows though it looks like a work not for its own sake --to answer that I plead the Talmud in Sanhedrin about mekalkel damaging which to Rabbi Yehuda is patur/ not liable and there a puncture in a wound is considered damaging--so no question on the Rambam even starts there.
