Originally Posted by MadQuilter

Sashing was my first idea too. If you use the same light fabric as in the background, it will look like your blocks are floating. That would look lovely.

The other option (as already mentioned) is to rotate one block by 90 degrees clockwise. That now aligns the adjoining point sections so one is pressed inward and one is pressed outward. Therefore they lock. On the next row you'd have to alternate.

The final option is to accept that they don't nest and sew them together as is. Yes, you'll have a bulky seam but that can be pressed/beaten into submission.