I like the idea of white setting triangles.

We would use white since you used white for the sashing strips

I like white with a dark binding

I have a different suggestion. Move the yellow ones into the inside of the quilt, then use a piece of like they suggest to fill in the tip, then the yellow on the rest. For borders, I would make a white small one, then a yellow, then to end in white.
I would love to see a pic of your little quilts to the left of your pic.

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*** Yellow or Beige.
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Perhaps add a white sashing around all the blocks, then add in triangles of several of your favorite lighter colors. Add a white border, then a dark binding.

I like the arrangement - I think your placement looks great.

As for the border and triangles - I too would use white - but for the borders - I might make it a three part border.
Border 1) small White ( maybe 1" to 2")
Border 2) small dark - or dark random scraps sewn together
Border 3) a wider outer white border
Binding ) dark or even a scrappy binding

I would use either white, or if you don't want solid white, a small print with a white background and flecks of color.

Looks great, I see at least 4 blocks that have black in them and also burgundy, I think I would use either of these to make my four corners, try those and see what you think. I don't know about what color I would use other than white I like the white. Have you considered sing a flange in your border? That might really look nice. I have used a flange border on several quilts and I think they made the quilts pop.

Looks like a lot of suggestions and many for white... I just want to say I like your quilt and looks like it was a fun mystery.