It's good that you trust your LFS, I have 1 that I trust very much also. It doesn't mean I can't misunderstand something they've said, nor does it mean they are 100% correct 100% of the time.
Your point about the water left behind, while is true in the way you phrased it, it has nothing to do with the points made above...a 50% water change is a 50% water change...if someone hasn't taken into account all factors properly then it wasn't a 50% water change, but whatever % it is will result in roughly the same percentage of nitrate reduction.
I am not in the group you describe as " because you are all concerned about maths and percentages" The math and percentages are for the benefit of others so that the process can be understood properly.
To say that a 50% water change won't reduce the concentration by 50% because it's a logarithm..just makes no sense, and flies in the face of the basic math. Had anyone said...hey don't forget about the water in the pumps and filters...then yes I would have to agree that may change the percentages...of both the water change and the nitrate reduction...however that has nothing to do with a logarithm.
I can't buy into this logarithm theory without more info to explain, why the simple math is wrong. So I guess we can agree to disagree.
The original post is asking "Can I be doing bigger water changes to make this go faster?"
The answer is yes as long as the pH and temp are appropriate. Some folks say dropping nitrate too fast can be detrimental. I've never seen this, someone may chime in who has with more info.
I'd recommend a 50% water change, see where that puts the numbers and then go from there.