If that is the case, I imagine it is because your liver provides a lot of it's stored sugar it shuts off when a new carbohydrate, low you say, arrives!
From my understanding of keto this is what is normal to happen!
I have only been borderline diabetic due to TXP drugs I take. That was adjusted with pills and my diet now seems to cope without pills. I have recently come off a keto diet. I needed to lose weight and other stuff. Worked well with intermittent fasting.
I do not think you can control the amount the liver puts away for rainy days, as it were?
As you say, maybe the order and timing of what you eat?
All the best Michael
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“ Every moment happens twice : Inside and Outside ..and they are two different histories ..!