I will try not to wonder off topic and give you my response based on your questions.
Firstly, Can one build a complete, coherent, comprehensive world view based on what science can tell us?
I would say no. Because what about moral, learning right from wrong, is that science? I don't think science can teach us that. How can one have a world view without knowing right from wrong?
Does science deny that there are any other paths to knowledge or truth?
Yes and no. Science is experimenting and exploration. There are many paths to knowledge and truth until science proves that there is only one. If science is wrong, then the paths open up again, but some people will say that the paths are always there, we just have to find them.
Can science teach us about the whole or reality or part of reality?
I think that science can teach us about the whole of reality. Because the reality in which we live is science.
Does science tell us anything about meaning, about purpose, about value?
No. Science can not tell us these things. These are based on life experiences and religious and philosophical beliefs. Everyone decides differently, there really is no universal answer about how we are supposed to answer these. Everyone will tell a different meaning for life, a different purpose, and different values that they hold.
Does science provide a coherent picture of human experience?
Again, yes and no. Because we can explore all the scientific discoveries about what we have experienced and discovered. No, because everyone is different and had many different personal experiences that science cannot explain.
This is just my input on the situation and as far as your last question is concerned, I feel that Poppers makes more sense. Science is about not knowing and the exploration to discover new things. It's not fun to already see and know everything.
Great post btw.