Yes, I would do that. It's likely that the base fabric is not the best quality either, so stabilizing them all would definitely save this work for a longer time when you are finished.

At my guild we have been encouraged to use a very light weight fusible behind all our base blocks before doing any redwork as it help to hide the tails, etc. of the stitches. I really like the look that this idea has given my work.

Since you have already begun the stitching, try it on one block first to see if you can get a good flat fuse on the fabric. Otherwise you might want to fuse first THEN stitch the rest of the blocks. Not sure how that will look; you'll need to compare I suppose. They sure are cute though!

Jan in VA

These embroideries remind me of the first kit I got for Christmas when I was a small child about 7 -8 years old. That would've been in '57-58". Much like some blocks of redwork I got at an estate sale also.

I agree with Jan, you would have to go with something really fine though. I love the look of the snowballing, embroidery never shows up too well on computer monitors, just be sure in your own mind (and visuals) the embroidered blocks do not get lost with the vibrancy of the patch blocks. You may wish to consider using solids?

I like the idea of using nine-patch blocks with these embroidered blocks using soft colors. They are so pretty.

What type of interfacing should I use? I picked up a yard of this to try out today. What do you think?
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Since the hoop outline cannot be erased by either heat or water on these blocks, I decided to use the same green to disguise it & frame the pictures and try to give it a "finished" look.
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The fusible interfacing I've use says "featherweight" or some other word to mean ultra light weight. Also from Joannes.

Did you try dampening it from the back ONLY on the hoop lines and then pressing? But, I think the hoop markings will eventually relax out.

I found the backing to this project. What do you think?
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Sorry, not the minion...

Antique: at least 100 years old
Vintage: at least 50 years old
Your blocks are lovely! Thank you for sharing!