I know that you have worked diligently to reduce carbs in order to get your blood sugar down. You will find it difficult to gain weight with a zero carb diet. My suggestion is to first grant yourself some slack on the whole carb thing. Eat enough carbs that your blood sugar is 140 mg/dl 2 hours after meal. Don’t eat zero carbs so you can be at 83 mgl/dl two hours after meal.
Next, you need to eat MORE! You need to start a food log. You should target at least 3,000 calories a day, perhaps even 4,000. You need protein. I’ve said this before, eat protein at least 1-1.5 g/ pound of bodyweight. I bet that once you write down what you have been eating, you will be surprised at your drop in calories when you dropped so many carbs in your diet.
Finally, I would recommend that you decrease the running and start some weight lifting. Endurance exercise can be catabolig and you really want to increase your weight.
There are many here that would kill to be in your position weight wise, but you would certainly be healthier with more lean body mass.