Hi,
Here is another option for you:
start your tie from the back side, take several stitches close to each other but not in the exact same holes. I like to place mine like I was stitching a box - one stitch on each side. Stitches are in a very short length, and really close together. After each stitch, tie a square knot. There will be a square know between stitches 1 and 2, between stitches 2 and 3, and 3 and 4.....

This only works if you are using something fairly light weight to tie with - pearl cotton works great and is available in a really wide range of colors, or a 'sport weight' yarn that can be machine washed.

If the fabric will 'buckle' between a knot, either your stitch is too big or too far apart.

After the last knot, I like to do one more - from the end of my last knot I will enter the fabric on the side of the little square of knots away from where I tied the last knot. This one serves to 'cover up' all of the others.

Ok, got that last knot complete. Don't cut your thread off yet. Instead, take one more stitch with your needle. Insert needle right next to the knot, but don't bring the needle out through the front. Instead, let the needle travel through the center (batting layer) for an inch or so, then bring the needle back up on the same side you started on - the back side in this case. Now, pull on the thread slightly until you see the knot starting to move. Now clip the thread close to the fabric. Your tail is now hidden in the middle layer.

You could use your sewing machine to make the 'ties'. Put the machine on bar tack and then use that as your ties. I would think that would leave a small stiched spot with no fuzzy 'ties.