The question of what an "appropriate" death for Littlefinger would've looked like leaves me drawing a blank. He was the smartest person in the kingdom, so there's just no death that wouldn't have left behind the question of "why wasn't he smart enough to see that coming or at least get out of it?" Considering that, it seems to me that the next most appropriate way for a person like him to meet his end is by becoming a victim of his few weaknesses. Littlefinger had a weakness for Sansa and also had an ego that may've led him to believe that the girls, particularly Arya, were easy to manipulate. Because of those two things, I think that it's plausible that he wasn't as careful as he would've been in most other situations. Lust and underestimation seem to me like entirely plausible and classical reasons for even a genius to be done in. Perhaps it could've been written a little better, but the general idea makes some sense to me, at least as much as any other possible death.