Well, Birdeen’s call, you have introduced a nice one here.
I think is that this is similar to the ‘come’ discussion on the other thread. It should produce an lively discussion. There is little doubt in my mind that ‘let’ in your sentence was originally a verb (I’ll ignore the ‘auxiliary’ for the moment). What it is now will, I hope, lead to some interesting points.
I will restrict myself in this response to questioning a couple of points you made. I look forward to reading your responses.