Keep the opposition.
1. Kf2 Kf4 2. Re1 Ke4 3. Kxe2
2...Kg4 3. Kxg2
1. Kx Ke4 2. Kf2 Kd3 3. Rx
Instead of 3. Rxc2, why not Ke1?
ahah, i know this one (was made by Reti iirc), it's pretty amazing. hope you continue to post these~
spoiler: white can force a way to capture one of the last two pawns with check.
1. Kf2 Ke4 2. Kxe2 Kd4 3. Rg1 Kc3 4. Re1 Kb2 5. Kd2
3...Kd4 4. Re1
1.Kxg2 Ke4 2.Kf2 Kd3 3.Ke1 doesn't White win?
It does. But looking closer, you notice that it would be a draw if white had the move, and the e-pawn is useless.
But 1. Kxg2 Ke4 2. Kf2 e1=Q+ 3. Kxe1 Kd3 is zugzwang and (dead) draw.
Wow. Nice study!