Iceblossom

I had to google that Jack's Chain -- Oh my goodness! What a fantastic (and daunting!) project.

The way I work I would probably consider appliqueing the blocks onto square backings. With a hex, two sides will be parallel to each other. When you put them together the parallel 9 patches will meet, and the backgrounds should form into stars. If you do have 20 blocks, that is 4x5 so a nice layout. (edit for clarity I hope: The 9-patches will be in the center top and bottom of the new block layout, the original sides will be pointed, the new square background will be a V shape that will form into 4 pointed stars)

If slightly less/more, you can use the finished 9-patches to make a filler block or two. When I work with vintage blocks I try very hard to not add much to them and I do all my additions with a different colored thread and if I have to add fabrics I keep them consistent with what is in the top, but clear where mine are, so for example if I had to make 4 blocks I'd put them in the corners and use the same fabrics in them.

With the individual 9-patches you could put them into sashing, but you would lose the all-over stars from the background. If they are all identical you might want to take the center rows apart for narrow sashing, matching those center rows to the parallel 9-patch blocks so you get the correct light/dark sequences. Or I'd make them into a border or a top/bottom row depending on how many you have, but I'd use them in the same project, on the back if necessary. (My current vintage project is a tiny little hex grandmother's flower garden I got at the goodwill for $6.00! It was huge but one row was only 9 blocks while the others were 10-11. I took off the 9 block row and will put those hexes on the back.)

The nice thing is that you don't have to do anything with them right away. Inspiration may or may not strike, but either way you will be thinking of your mother.