About |25.v17: it looks to me like a distraction tactic, and it worked. But it's no better than |25.r18 or |25.t18, because if you just ignore it and play |26.s15, then what comes next? Whatever move 27 is, it must involve a link, because if it doesn't, then 28.u16 will work. The possibilities then are few enough to enumerate: |25.v1726.s1527.t1428.t13 - doesn't work, 27.u1528.u14 - doesn't work, 27.w1528.t13 - doesn't work. That's it, then; the curtain should go down on White at this point.
After |27.u15, the possibilities for Black playing south aren't very good, because White has multiple threats, most importantly R18. 36.S20 still looks good for White: 37.u2038.w2039.s19. So, after 27.u15, 28.q14 was weak; kpato needed some kind of combination threat, to punch a hole in Carroll's dotted line. Maybe 28.r11, threatening p10 or q14. If 29.p12 then 30.q14, and if 29.q15 then 30.p10. That looks pretty good for Black.
After |27.u15, the possibilities for Black playing south aren't very good, because White has multiple threats, most importantly R18. 36.S20 still looks good for White: 37.u20 38.w20 39.s19. So, after 27.u15, 28.q14 was weak; kpato needed some kind of combination threat, to punch a hole in Carroll's dotted line. Maybe 28.r11, threatening p10 or q14. If 29.p12 then 30.q14, and if 29.q15 then 30.p10. That looks pretty good for Black.