"Glucose concentration was lower (4·09 (sem 0·10) v. 4·89 (sem 0·06) mmol/l, P < 0·001) and β-hydroxybutyrate concentration was higher (1349 (sem 139) v. 234 (sem 25) μmol/l, P < 0·001) after the high-protein compared with the normal-protein diet."
β-hydroxybutyrate is a ketone body.
Note that this contradicts your statements that GNG will kick you out of ketosis. It absolutely will not.
To repeat: GNG is constant, regulated by ketones, and its relative level is not driven by protein demand, but by glucose depletion.