What if you just closed Nerdtree before moving your splits, thereby avoiding any of the following problems:
nnoremap <C-W> :NERDTreeClose<CR><C-W>
Once you're done manipulating split screens, run Nerdtree again. If you need to be a fantasy, combine closure, spinning splits, and rediscovering Nerdtree in one mapping, something like:
nnoremap <C-W>r :NERDTreeClose<CR><C-W>r<bar>:NERDTreeToggle<CR>
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