From watching other people play the game and just practicing the jumps a lot I found some easy ways to make the jumps a lot more consistent, at least for myself. In my recent PB (under 3 minutes), I used my tricks to successfully make the jumps in one try. https://streamable.com/nxydi

The slide skip is at about 1:04. When I have latched onto the top part I will swing myself below so that I am past the halfway point and then in one fluid motion will swing around and push myself off at the same time. In the video I didn't swing past the halfway part very much (basically just straight) but if you're just starting out I recommend using the full swing and exaggerating the movement.

The hat and anvil jump is at about 1:50. For the hat jump I will completely rest the pot on the ground, preferably a little bit to the left. When I'm ready I lift my hammer up about a quarter of the pots height and I will slam it down, at the same time pulling the mouse to the left a small amount. IMO the anvil jump is the easiest if you're using the method in the video, otherwise it can be the hardest. What you do is position the pot close to the edge of the anvil, but it doesn't have to be perfect as this jump generates a LOT of power. As seen in the video, you will bring the hammer up and to the right and then slam it back down diagonally, essentially a larger hat jump.

Hope this helps!