OMG your pigs are sew cute!! I love how you put them on Churn dash blocks that are monochromatic. I can't wait for you to picture the whole quilt.
And yes they look like pigs as they are, in fact you could even leave off the curly tail as there is no question these are pigs. And if they are fused then I also agree with annaquilts in how to sew them down with a clear monofiliment thread and small zig zag. The monos they offer today at better LQS are not like the fishing line of the past. The threads are fine like human hair and some have no reflection so they are indeed invisible until you are right on top of them. You could also use a silk in a neutral gray that would also virtually disappear on the gorgeous batiks.
You siggy line states you have a LA so you could LA your curly tail and little details in the quilting if you still feel the pigs need it.
Please make sure you post a pic of the whole pig quilt when done.
PS I too am curious why you feel compelled to make a pig quilt. Do you just like pigs? Charlottes Web a favorite of your youth? The applique you have certainl reminds me of one of the illustrations of Wilbur.