I felt hopelessly lost through most of this game - not sure what I did wrong in the beginning but judging by the situation, I must've played something awful.

The 20.i14 21.g14 exchange seems to clearly favor white. Wouldn't 20.i12 be much better for black?

20.i12 21.k13 22.h15 23.g14 24.g13 25.f12 26.f10 is a black win
20.i12 21.j15 22.k13 likewise

Am I missing something?

I did not really analyze but maybe |20.i12 21.m14

With threat on o13 and m18 for white

Florian, I think 20.i12 21.m14 22.l15 is still good for black?

20.i12 21.m14 22.l15 23.o13 24.t16 looks ok for black
20.i12 21.m14 22.l15 23.t15 24.p12 does too?

|20.i12 21.m14 22.l15 23.t13 ?

Ahh, you're right! 20.i12 is quite spectacular then :)

|20.i12 21.m14 22.l15 23.t13 24.u14 25.u15 26.n8 27.s11 28.r5 29.r6 30.s7 31.q4 32.p5

Actually, |20.i12 21.m14 22.l15 23.t13 24.u14 25.u15 26.n8 27.s11 28.r5 29.r6 30.s7 31.q4 32.p5 33.o5 34.q6 35.n7 36.m13 37.o8 38.o7 39.n9 40.q5 41.r7 is a draw.

But 22.n12 23.k15 24.k14 25.k13 26.k18 27.i14 28.g18 looks winning for black.

Again, I made a mistake. |20.i12 21.m14 22.n12 23.k15 loses, but 23.l16 wins.
So it looks like 22.l15 is the best answer to M14 and it leads to a draw.