I have batting tape.

Is it fairly thin? .... any that I have seen I might hesitate, for the extra bulk it would create.
What I am getting at is ... would that show on your finished quilt??

BTW EasyPeezy... you have me intrigued as to what pattern you are making.
Any links for us to see ... Please? and Thanks!!!

I would start with a light weight stabilizer to help prevent stretching.

What about French fuse as a lightweight stabilizer.

All you need is 1/2 wide. The batting strip will be in the seam when sewn.

I'm thinking either too much foot pressure, or your stitches are too tiny and need to be longer.

Elmer's washable glue! Seriously, once you try it for bias edges, perfect points, etc, you will never pin again. : )

I used it for 17 inch hst with no problems.

That was my first thought that your tension was too tight and distorting the seam. My largest HSTs were 7 1/2", but no problems.

This is the one that makes the most sense and is economical. Test run one to see if it accomplishes what you intend. Also, always keep you hands lower than your needle, allow the machine to do the work.

If you are doing the square with stitching down middle then cutting and you are having a problem with stretching, there is a push/pull issue involved. It can be you are doing it without realizing or your machine is doing it. If you, resolve it by only touching the fabric with your finger tips and see if that helps. If it is the machine, you are going to have to adjust some things. Grab some scrap cotton fabric and start sewing on the bias. Try using a walking foot to see if it evens out the feeddog movement. And you can always fuse a strip of interfacing to the seam line before stitching (1 " piece and then mark down the center). The good thing is that once you have figured out why it is happening, it won't ever happen again!!