I think the block you show is a disappearing hourglass, which is made up of HST's instead of 4-patches. MSQC has a tutorial video on it here:
https://www.youtube.com/watch?time_c...&v=xXggafOP230
Since you want a specific finished size, I would use a different method to make the HST's than what Jenny demonstrates. Her method gives bias edges all around the block; I would use the 8-at-a-time method instead, so that I don't have to deal with that bias. If you start with two 15" squares and use this method:
http://blocloc.com/wp-content/upload...rt-for-HST.pdf, you will end up with eight 7" HST's.
Then follow the MSQC video from 4:05 onward. Join 4 HST's into an hourglass block, cut it into 9 squares, and rearrange as you did before. This should give you a 12.5" finished block.
It's late, so I might have made some huge mistake somewhere, but I think this will work. Good luck!