As part of the discussion, did you press the fabrics to one side as is often recommended or did you press your seams open? I press open for a number of reasons, seam thickness is one of them and while many people love it, I don't personally like working with flannel as being too lumpy and too collecting of pet hair
I think it looks really good to me just as is and that indeed you are being a bit harsh on yourself. Among other names, that is a Quarter-Square unit, or an Hourglass or set like that Broken Dishes. Your workmanship looks lovely. You can indeed just cut off that outer edge and put in a batting, replace the back and bind with binding instead of the birthing method. Be warned though, any time we sandwich like that there is some movement and your original back will be too close a fit without causing yourself a fit to put it together. Start with a larger back, we generally recommend 2-4" all around pre-quilting.
Many machines have a "serpentine" stitch option and many quilters love this. I used it recently for the first time just this last week (my old vintage machine did not have the option). The advantages are that it gives a fancy effect to a simple grid and in this case you would be criss-crossing the seams which will help flatten them out.
Here's a picture of my project which used a terribly thick batt, but it was what I had that fit the top. As a beginning quilter I'd say stay away from "high loft".
Quilt help needed, Soft n Crafty