I can fill my boots with protein and it has no effect on my BGL, others on this forum need to take ridiculous amounts of insulin to keep their BGL in check. Honestly like there is bread hidden in the meat! I suspect that you don't yet know whether protein has an adverse effect on your BGL?
If you're not wanting to increase your carb intake (which is understandable) then your only other option would really be fats, protein and milk and dairy. These can affect BGL but if you're looking to gain weight then this might be your only option. I'm no dietician so can't really advise that well.
What about increasing your carb intake but with better carbs? Such as seeded breads, green veg, lentils, nuts, etc?