I got this technique to work extremely reliably last year. However there were a bunch of caveats: 1) Firstly, you must institute a check that the multiple choice tokens dominate the output distribution. They should sum to 95% or more, ideally 99%, or the LLM is not following instructions properly. This is also the problem with constrained decoding - if the LLM really doesn't want to output a valid answer, the one you extract will not be high quality. 2) You need to ask it multiple times, permuting which option corresponds to which letter, and average the results. LLMs are surprisingly biased towards picking "A", especially if they're otherwise not sure. 3) For the same reason, performance improves if you frame the prompt as if it were the middle of a quiz. "Question 1" carries baggage that "Question 12" doesn't. 4) You must be exceedingly careful with tokenization.
But when all was said and done, I got a general purpose A/B classifier that gave high resolution quantitative output for the cost of a couple dozen tokens ingested and a couple inference passes.