My sense is that you're asking two questions in one. There is an appeal process where the same criteria are imposed and we are only looking for mistakes by the officer who made the decision, and then there is a compassionate appeal where we are looking for someone to make an exception to the current criteria, to let someone in despite the current criteria. I think you lean towards the second of the two, which is a very different process than a judicial type of review, which imposes the same criteria. I think your fundamental concern is with the criteria for admission.
I'm not saying you don't want an appeal. Appeals are useful, but I think your fundamental concern is with the criteria rather than the appeal itself.