Its amazing that you kept at it after the material gave you such trouble.
Speaking as a professional picture framer, I will rarely use any hard material like oak for the very reasons you experienced. Bass is a highly favored material because it machines nicely, doesn’t shatter unless I’ve done something really stupid and is reasonably priced.
I will be so bold as to suggest that you consider using a mat board around the art. It enhances the appearance of the picture. But it does require a deeper rabbet to accommodate all the layers (glass, mat board, art and a support of some sort).