Oral exams scale fine. A TA makes $25 per hour, and an oral exam is going to take an hour at most. I absolutely would not accept a $25 tuition rebate in exchange for having my exam administered by an LLM.
But you'll accept the results of an exam for a (in the US) $1000+ course given by a TA that makes about the same as a delivery driver? And you'll trust their assessment of the results? There's so much wrong with this idea, I don't even know where to start.
Obviously the session should be recorded & transcribed. If you take issue with your mark, you can escalate it to the professor, same as you would for a written exam.
If you're looking for suggestions, I'd love for you to start with a problem that isn't trivially fixable.
