>

Then the issue isn’t the signage. Your issue is with the actual laws. Changing a sign isn’t changing a law. The painting/signs has nothing to do with it.
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Who has the right of way in that situation?
The reason some people think they are in the “right” lane is because they are. The drivers entering the “right” lane are legally responsible for yielding. There is no legal responsibility to let anyone in, ever. It just doesn’t exist.
Zipper merging is more of a social norm where people take a “treat others the way you’d want to be treated”. >

You’re proving my point. Zipper merges shouldn’t be a “social norm.” They should be part of the traffic code, which I believe will lead to safer and more efficient traffic flow. 
The way you’ve described it here is exactly how people are conditioned to think based on current signage and paint markings. My view is that if we changed the signs and paint, traffic would be safer and more efficient. 
In my ideal design, neither lane would have “right of way”. They both need to make sure the space is clear to merge. If an accident happened, the default result should be that both drivers would share fault for not ensuring the space was free to merge. Obviously if there are witnesses saying that one driver was driving aggressively, or the front of one car hit the back of the other car, then that could outweigh the default assumption of 50/50 liability.