I'd do the no match of the seams...think bricks in a wall.... and add sashing. Pick a totally different fabric for the sashing and use it for the last, outside border and it will all be tied together. FYI...years ago, I made a quilt similar to yours, except that I added appliqued circles of chenille fabric. The child I made it for is now 8 and loves this quilt to this day. I wish I had made it larger. She loves the feel of the chenille. Guess I'll just have to make her another one.
A comment about a serger...it is really hard, as you have found out, to keep seams at a quarter of an inch with a serger, and there is really no need to use the serger. All the seams are on the inside and, though some fabrics may ravel a bit worse than others, you are usually putting a back on it quick enough not to have too much trouble with the ravels.
We, as quilters, are our worse critics. I still want my quilts perfect, but my grandkids don't even see my errors. They just love that I made it for them. The child you are making this for won't care if it is a bit wonky or not perfect, trust me.