Hi switch
I have had the same problem, but have managed to put on a stone over the last 8 weeks. I am 6'-2", went down to 11 3/4 stone, now back up to 13 stone.
I have done this on a LcHf diet, by eating more meat, plenty of double cream, cheese, butter, aubergines, frying all meat and veg in oil or butter, try mushrooms fried in butter. Plenty of Mayonnaise on salads. A beer during a meal.
I have found this has not effected my daytime BS readings, but my overnight / pre-breakfast levels have gone up a little, I think caused by the extra protein, which takes a long time to go through the system.
Only down side (for me) is that it does cost more to feed yourself on 'more' meats, cream etc.!!!!!
Good luck