Recourse for patently unfair make-up exam?

Given that exams are difficult to create, especially make-up exams, it is just possible that it will work out when the instructor sees the results. I doubt that it was any sort of 'retaliation'. Wait for the grades and have a conversation.

It is too early to take action until you see the actual results and their effect.

Let me note that for some sorts of exams, writing intelligently about the problem is enough. If the problems are especially difficult then it may not really be possible under exam constraints to find a proper solution. But if what you write is "sensible", and demonstrates that you have the required knowledge, it may be enough, depending on the person interpreting the results. In any case, it is pretty much impossible to treat the results as "equivalent" to those of the normally given exam. A sensible instructor will recognize this.

It's been a long time since I took a university course but I wonder if you might be unduly concerned about the makeup exam? From what I hear, professors are very prone to use Bell curves when marks aren't what they hoped for. For what it's worth, I once taught a database course at a college when a friend who had the gig normally had a conflict and couldn't do it. I wrote a pretty straight-forward exam with no trick questions or indeed anything terribly challenging but the marks were disappointing, mostly in the 60s and 70s. I'd already heard vague general rumours about colleges and universities belling up marks so I asked if I was supposed to be belling up the grades. The department head strongly encouraged me to do so. On reflection, I decided that the exam was perfectly fair and I could not justify altering the marks; I submitted exactly the grades the students had earned. I never heard further about it beyond one student expressing his disappointment that he hadn't gotten a mark of 90+ as he had with the other courses in the program.

If Bell curves are truly rampant in academia, then this may well solve your problem.