One of the blanketeers in our Project Linus chapter makes several pieced fleece blankets each month, and they are also backed with fleece. They look great!
Concerning wonky fleece: I buy and prep fleece for Project Linus blankets - tied, braided loop edge, and crochet edge. There are many bolts of fleece that are just plain wonky to begin with and nothing you can do will help, so it is a good idea to look closely at the fleece before buying. You may have to roll off a yard or more from the bolt to see it, but look at the design and also look at how the selvages are lining up with each other.
Once you trim the selvages, hold up the fleece with two top corners together and see if the sides line up when hanging freely. This procedure is similar to finding the straight grain on a piece of cotton, but at least with cotton you can see the threads. Knits aren't so easy.
Also, I would recommend anti-pill fleece, which usually looks much better than other fleece after several washings.
Making a small quilt or lap robe is an excellent idea.