a simple repair...( should be)

I dropped this piece of blackbutt on the corner. I steamed out most of the damage using an iron however the fibres on the corner were broken. The bit that was steamed looks poor and you can see the pores. I am pretty sure that planing will remove this.
According demonstrated in this fine woodworking video at about 3:25 Fixing Woodworking Mistakes - Fine Woodworking Video i have planed the corner flat to accept the piece to repair it. Having done this once before i thought no drama ... which there wasnt for this part. See photo
My problem is that when i try to remove the matching piece from another piece of blackbutt the timber is splitting. It is also a bit rounded with broken fibres rather than what i am assuming is shown in the video is straight. ( video shows the result i am aiming for at 4 minutes). I have tried a few different pieces with the same result.
Am using a hollow ground chisel as is the video
Any ideas to get me back on track would be appreciated.

The wood whisperer shows a similar approach on this vid with a rectangular piece of scrap at about 1120 in this vid https://m.youtube.com/watch?v=k-TWPlUI2jM

Hi Pacman,

personally I would just use a saw to cut the (oversized) replacement piece, and sand the surface to be glued on a block wrapped with sandpaper.
I've done this with success with a couple of abused chisel handles, works fine - don't be afraid to make the replacement piece significantly oversized, it makes the whole process easier.

hope this helps, Jeff

Thanks Jeff I will try the saw to cut the oversized piece