The only type of stabilizer I would use with that is wash away. My walking foot would get in the way and break the needle.

Three layers of fleece is quite thick. Are you using a walking foot to help feed the applique thru the machine smoothly??

Walking foot is essentially a zigzag foot with feed dogs. If it wasn't meant for zigzag then it would be a single hole foot. Now not all machines have the same feeding power, some brands are just sturdier than others. No matter what the brand, you should service your machine every three years unless you are sewing everyday

I have a Bernina Activa and I am able to zig zag with my walking foot with no problem. Can also satin stitch or embroidery stitch. You have to test first because the design may look different since it is spaced differently by the walking foot but still makes a nice design and excellent for thick types of appliqué. I always use a Superior threads
top stitch needle on something like this I would use a 90/14. I don't think ball point needle is the correct type for this. I only use ball point on knits. Hope this helps you.

Make sure that your bobbin is wound correctly; I have had this problem and when I wound a new bobbin (slowly) the problem was fixed

I agree with the others, it needs a stabilizer. Let us know how it worked out.

Personally, I find satin stitching a pain, I've switched to blanket stitch and love it. Do you have that option on your machine

I would use a different foot; what about an open-toed foot so you can see where you are going and how it is quilting the edge. You might also stitch down the edge of the penguin all the way around so that it won't get scrunched up and skip stitches. Just a thought. Post when you figure it out--many of us might try the penguin too.

You might check the area underneath the bobbin case. I took some dental floss and was shocked at the amount of lint collected there. Also, a wash away stabilizer can be used on top of the fabric to help keep the stitches from sinking in and maybe make stitching a little smoother. (Like you would use to stitch on towels.)

use some paper on the back side of what your sewing