Iceblossom

In the old days many quilters did resolve this by basically applique combined with folding. That is, you start with a long strip and then you cut down to your seam line at the bottom of each Vs and fold the sides to make the triangle points. The weak point is there at the bottom and fairly easy to reinforce with hand stitching or I used to group with one lady that did the most fantastic machine applique with tiny nylon thread and invisible to me stitches.

My last project was just a small simple baby quilt but I chose to do LeMoyne stars and set in both the square corners and the triangle sides because I felt I could use some practice with those Y-seams. And I did! But I'll go back to avoiding them for awhile again.

I also do origami as a hobby and so do a lot of folding... How big are these points? I wouldn't want to do tiny but I can almost visualize the movements to do what you want. Think of how mitered corners work but that you'd be working from the underside with the outside flipped out instead going around the corner. I know, that is more obscure than a lot of my comments and partly because I don't quite have it yet, but I think it would be doable with say a 3" triangle for the length of a border might stress me but would be doable. Once you had it down, it would probably be worth posting a youtube video on how to do!