Cut.
I finally understand what he's going for, and why I didn't see it at all before. For some reason, after I played my jump at M5 to practically kill off K4, he decided he was going to make K4 live. At the very least, that's bad timing, because there was better opportunity for K4 before I played M5. More importantly, it's way too heavy. What would black have done if white ignored K4 for 50 moves? Probably nothing with respect to K4. So why should white immediately try to rescue it?
If you do feel a need to rescue K4, you should keep in mind that the stone itself is small. That's why I was suggesting crosscuts all over the place - the easiest way to stop your opponent from claiming a big area is to force them to make a choice within the area and take advantage of whichever direction they don't choose. Before he made these exchanges like kick and Atari, K4 was really light, so he could offer it as an option. Now, not so much.
The sequence I expect is 10-5 Atari, 10-7 connect, 11-4 connect, 13-5 connect, 12-2 double Atari, 13-3 connect. He then has to live with 9-6, 10-5, 10-4, 11-3, and a loose 12-2. It's probably possible, but we're looking at a heck of a lot of influence for me by whenever he lives.
Actually I see some potential ko variations on the left, so I think he shouldn't exchange the 11-4 connect and the 12-2 Atari, but save them for potential ko threats to help him live. Also, I'll have a harder time taking advantage of liberty shortages, potentially. So probably he should exchange the atari (since he's already committed to K4) and then play on the left somewhere. It's getting interesting!
