I know of no other way to stimulate maximum glucagon secretion than to eliminate carbohydrate intake. In the absence of dietary carbohydrate, there will be no more than the usual tablespoon of glucose in the blood, which is the level gluconeogenesis aims at.
A lack of carbohydrate in the diet will also drive your insulin/glucagon ratio as low as possible, and the glucagon will stimulate ketogenesis. The minimal insulin secretion stimulated by your protein intake will keep gluconeogenesis and ketogenesis under control without inhibiting them, so you won’t need to fear hyperglycemia or ketoacidosis.
You may find that the only way to drive your GKI so low is tosupplement your liver’s production of ketone bodies with an exogenous ketone supplement. It would also be wise to refrain from activities that would consume the ketones, so that they can remain circulating in your bloodstream and provide a high reading.
If you are trying to control cancer with a ketogenic diet, be very sure that the type of cancer you have is not one of the ones that thrive on ketone bodies. Not all cancers respond to the Warburg Effect, apparently.