Seax can have a variety of tip designs and still be considered a seax. If I remember correctly a broken back Seax is sort of like a clip point. I am not sure what you meen by "toothpick" design as I have seen things from huge bowies to tiny slipjoints be described as "toothpick" (Arkansas Toothpick, Tennessee Toothpick, Texas Toothpick). Some of these "toothpicks" have spear point, most had some kind of clip point. So then a broken back and a "toothpick" seax would both be clipped pointesque blades?
A tip isn't what determines if a blade is a Seax or not. There are seax with many different types of tips and no one type is more a seax than another.