I've been working away on this same Split 9-Patch and making decisions on the border. It seemed that a WHITE border was my best choice, but it looks kinda wimpy and washed out. I've used this technique before, when the block seems to stop too abruptly, and some version of the block would look good repeated out into the border. I wanted my border to be all one piece, not broken up into segments just to add the blue or red triangles. I think my fusing method saves time, (assuming you remember to put the fusible on the correct side at the get-go!).
I've faced the triangles with fusible interfacing, turned them right side out and INSERTED that unit between the border fabric and the quilt top. It cuts down on the effect of so much WHITE border, and it also blends the block into the border. BTW, after turning, these can be pressed gently with an applique pressing sheet - what a great invention!
Be sure to configure the background border with enough room for the fused triangles. When the quilt top is finished and pressed, I fuse them down, then blanket stitch them permanently with invisible thread, before quilting.
The blue plaid is my last border. This is a humble scrappy quilt - those triangles in the border do NOT have sharp points - I can live with that. But ... what if a person made them roundish? Another possibility for another quilt.
Except for the borders, I only pulled fabrics from my 2 1/2 inch box. I also made 10 Spools Blocks and 8 other blocks from that same box. hmmmm, now the box barely closes at all!