You could finish very nicely as is in the form of a table runner and keep to your no UFO rule !

I am working on this right now. I have been trying to find a pattern for a particular fabric and this is perfect. But, I understand your problem. Because of the bias, the pieces all come out slightly off - no matter how careful you are.
I love the picture of the blocks on point. This will solve the slightly off situation (hide it in the sashing/solid blocks). The solid blocks will also let the fussy cut centers really stand out. I LOVE THIS BLOG!!!

I love the Exploding Star block and I don't believe you were intended to match the resulting points. Just square up the blocks and put them together any way you like. Put sashing between them or as yadroc did they are amazing. I'm using them on 2.5" squares to start and am going to use them to make a baby quilt. Take a look at the block again and see if you could just cut off those offending points as they don't affect the block at all.

Send a picture and note to MSQC about the challenges you are having with the Exploding Block. Jenny might have other suggestions for you.

When I watched the tutorial on the exploding block the points were not made. I am going to watch it again just to make sure. I would put sashing between the blocks.

Well this is kinda embarrassing, but after putting together a couple of more rows I discovered one of the problems was entirely mine...some of the seams at the ends narrowed making it off...I'm correcting them as I run across a wayward seam. Another reason for leaders and enders but I was chain piecing the 120 blocks so it was just my bad....they have gotten better. Quilting is teaching me lots of lessons..about life and quilting..learning to let go of perfection(to a certain extent) and trying new ways of doing things...

I watched a demo a few years ago on making this exploding block. She took the top square, set a ruler from one corner to the opposite corner and and made three short cuts with the rotary cutter. Then she put the ruler on the other corners and made just two cuts, so that the cuts did not intersect with the first cuts. Now, after the top square is sewn on RST, it's super easy to get the scissors into those cuts and finish them into the corners. No drawing lines and trying to get the scissors into the fabric.

I am making the exploding blocks and enjoying them. There is no planning except color values. I plan to put narrow sashing with small cornerstones between the blocks.

I think the sashing is the salvation with these blocks but it wasn't what I was going for...Have used up a lot of scraps though. Sometimes I think I can and do over complicate even the simplest of things...Halfway there so it's going faster. I really enjoyed making the blocks...something different... I will be looking forward to seeing all the different takes on this block...I know there will be some gorgeous ones..

Here is another one! Double Exploding Blocks. A friend came up with this idea.