I think you should still have the jump to the wall.
I don't like the feel of him stopping at the bottom and then climbing it.
I know what you mean but I was hoping (is that how it's spelled because it's not a pun) to use the jump animation that I've already got. The climb/heave animation starts when you grab on to the ledge and ends when you're standing up. I put in a token jump frame at the end but it looks like crap. My bad. I'll update the animation I've got posted to accommodate for the jump.
Edit 1:
This is (almost) what I expect it to look when you do a 8 block jump + ledge climb.
The actual jump looks better in-game with proper physics, I had to wing it making the gif-animation.

Edit 2:
The troublesome part is stringing together different animations as seamless as possible. I've got the running animation stopping on the frames where both feet are in the air which makes for a really nice jump animation. This means that the player changes which foot is forward for every jump which looks great. For this to string together with the ledge climb animation I added some frames where he's reaching for it like you suggested Arachne.
Edit 3:
Looking at these last animations I feel that it's a little stupid that you'd climb 3 blocks when you can jump 5 without climbing.
Edit 4:
I added block heights to the ledge climbing animation. while doing that I realized that the animation is inaccuratly displayed because the platform is not moving at a constant pace, nor is the space-man fixed in position which would be another way to do it. Now things kind of move at irregular speeds as a result of me winging this gif by hand.