Ignoramus26161 writes:
Suppose that I do eat an excess of protein, say 300 grams of it. Say
that I use 100 grams for maintaining my body tissues, that leaves me
with 200*0.58 == 116 grams of sugar produced.

Other way around. 300 * 0.58 = 174g sugar, leaving you 126g protein
to maintain body tissues. However, your liver stops converting
protein when it has enough carbs, likely leaving more protein for body
tissues.

Since the liver stops converting when it has enough, I don't think
overdoing the protein can have the same effects as overdoing the
carbs, so IMHO it won't make it not LC.