What would you consider to be a situation where the connection would be clear?
I thought about that question all morning. Good question by the way.
Well first things first I have to say your bannerstone/bilobed arrow motif notion has one thing going for it. As fancy atlatl weights (a tool for mighty warriors and hunters) , I could see most any self respecting warrior or hunter proud to have a bannerstone effigy item on his regalia. Assuming bannerstones are associated with hunting, then men would indeed covet the symbol. Now if the items are net spacers, spindle whorls or drilling counterweights, I get less enamored by the whole thing. People being people no matter their culture, and men being men no matter the culture; I just don't see a warrior or hunter wanting a cordage making tool or a drill weight on their head. I am not saying it would be shameful, I just think symbols have power. Our modern team mascots are fierce, strong and worthy of respect. Not to be trifled with. Bannerstones have to mean something powerful or aggressive; or they have to go as an effigy on defenders and hunters.
What would it take for me to accept it? A bannerstone found in a Mississippian era mound would open my mind. I might even go with a late Woodland mound. That would show me bannerstones continued long enough to serve as a symbol that was relevant.
Another option would be an artistic rendition that shows a bannerstone
without the bilobed arrow from the Woodland or Mississippian era. In this way it would show a progression of the concept. To me your suggestion that the bilobed arrow thing is a symbol of an arrow going through lungs. That makes perfect sense for a hunter/warrior.
Right now I think that bannerstones and bar weights were a thing of the Archaic period. For what ever reason they stopped being used at the end of the Archaic period. If they were indeed net spacers or drill weights or spindle whorls, then my question is
why stop using them? If anything, the need for such tools increased with the advent of the Woodland and Mississippian culture. The arts exploded. Shell craft was in high demand. I am sure the wealthy or high status folks had shell gorgets and beads. But I also think wood was used for these objects as well. Wood needs drilling same as shell and metal. Anything the people did in the Woodland period was pushed to its limit in the Mississippian period. Bigger, better, fancier. Shell, copper and stone craft were taken to extremities of what could be done. Nets and woven cloth would have been in huge demand. Commercial fishing at a city like Cahokia for example would certainly need a fishing fleet armed with nets aplenty. Populations rose at Cahokia and other Mississippian sites. If anything there was higher demand for drilling and fiber production than ever before. Clothing was largely woven - not leather. If bannerstones had other use then why didn't they persist past the Archaic?
My argument is simple, they are replaced as archery arrived. How that took place is still sloppy and has missing puzzle pieces. the timing is right - especially if as you argue archery is older than we think. It just makes the most sense to me. atlatls declined but didn't disappear. Bannertones were however, not needed to give an edge. The bow compensated by giving the edge needed thus making the bannerstone unnecessary. Feel free to disagree. That is just conjecture on my part. without a time machine . . . well you said it.
By the way, your thought about bannerstones being rare is a good one. If we get stark raving mad about they have to function for something, well, the fact is not everyone had one. Food for thought.
fun fun fun.