NFA state complexity for the complement of EPAL restricted to a fixed length
Hint: further break up the difficult case $\{ww' : |w|=|w'|=n,w\neq w'\}$ as a sum $$\bigcup_{i=1}^n \{ \Sigma^{i-1} \alpha \Sigma^{n-i} \Sigma^{i-1} \alpha' \Sigma^{n-i} : \alpha \neq \alpha' \in \Sigma \}. $$
In total there are $n+1$ cases (including $\{w : |w| \neq 2n\}$), so if you can implement each one in $O(n)$ states, you're done.