It's not the initial outrun that's the issue but maintenance
To give the answer to the original question...
Akatsuki-class range: 5,000 nm at 14 knots Nagato range: 5,500 nmi at 16 knots
I can't find the ranges at flank, the destroyers would likely do better at 20 knots, opening up a gap and trying to get away from recon aircraft range or waiting for nightfall before making some more dramatic maneuvers to lose Nagato completely...
