58% conversion is the max amount of conversion of protein to glucose in the blood from alanine and glutamine.
During the 1st 3 weeks it mandatory to get at least 150g protein and this isn't taking into account exercise, in order to prevent most nitrogen losses.
The reason fat "seems" to get you into ketosis faster is b/c you are ingesting a greater amount of fat, making more free fatty acids available to enter the liver and get converted to ketones, the greater amt. of ketones from a high fat intake is being excreted from the urine and showing "deeper" ketosis. BUT, understand that ketonuria (exretion of ketones from the urine, indicated by using ketostix) isn't indicative of kenonemia, the actually state of ketosis where ketones are shown in the blood. Showing "deeper" ketosis, (a darker purple) doesnt mean more fat is being burnt, just that more is being excreted, but one can be just as deep a level of ketosis minus the high fat intake. Basically the more fat u eat, the less is being burned from bodyfat, eat less fat and more is used from bodyfat (within reason, if one is starving on a Very Low Calorie Diet, less fat overall is lost from a slower metabolic rate). I'm not arguing either, just stating the facts. Its actually more beneficial to keep protein a little higher the 1st few days b/c as one adapts to a ketogenic diet more protein is necessary to prevent nitrogen losses, fat is protein sparing but only to a degree as a certain amount of protein MUST be eaten to be protein sparing.
EX study, 400 calorie diet of protein vs. 800 calorie diet, 400 cals from protein, 400 from fat. Both causes the same nitrogen losses indicating fat isn't anywhere near as protein sparing as protein and is mostly necessary for EFA's, test. production and to prevent too low a calorie intake causing a lowering metabolic rate.