It's not entirely clear here exactly what you're asking it sounds like a moral question as to how to apply Kant's ethics, which is how I've answered, but it could be a question about how far one can manipulate Kant's ethics without it no longer being 'Kant's', which seems an entirely trivial question which I won't engage with, so my apologies If I've missed the point.
Fair enough, but can't we amend the rule regarding lying to be:
"Don't ever lie, unless by doing so you are saving the life of an innocent person."
Yes, but only if you already believe that saving the Jews is the right thing to do and that telling the truth to the Nazis about where they are hiding is not going to bring that objective about. You have, in formulating such a maxim, already done the ethical work the maxim is pretending to help you do. You've already decided what outcome you think would be morally right (saving the lives of the Jews) and you've already decided what course of action will best bring about that outcome (not telling the Nazi's where they are). The point of the maxim is not to help you make such a decision, it is to help you justify it to yourself so you can live with the choices you make, as Bertrand Russell put it "without being paralysed by hesitation"
You could just as easily justify the decision (that you've already made) by utilitarian ethics (the most good will come about by saving the innocent from oppression), by virtue ethics of any kind (it is a virtue to defend the oppressed against violence), even by hedonism (standing up to such a powerful group as the Nazis to save innocents makes me feel like a hero which gives me a lot of pleasure). You make the ethical system fit your preferences, they will all require some manipulation of their inherent ambiguities to make them fit.
Are imperatives still considered "categorical" if they contain unambiguous universally applicable "unless-then" clauses?
Considered by whom? Surely this will depend entirely on a completely subjective interpretation of "unambiguous". As Jobermark points out "innocent" and "saving" can be considered ambiguous, but so can "universal law", which is, I think, the crux of the question. How detailed do you make the law? Is it lying to anyone, lying to authority, lying to Nazis, or lying to these particular Nazis on this particular day that you are universalizing?
These ambiguities are a necessary component of any ethical system, not a flaw, they are there because if an ethical system actually did tell us how to act in every situation, it would undoubtedly be so over-simplistic and prescriptive as to be completely unworkable within days of everyone following it. But perhaps more importantly, what kind of idolatrous zealot would dismiss millions of years of cultural evolution to follow the prescriptions of one random 18th century German?
If, when faced with actual Nazis (or the modern-day equivalent) asking about the whereabouts of your neighbours, intending to do them real harm, anyone really wishes to rely on the advice of just one person against all their instincts and culturally learned values and judgements, then good luck to them. For the rest of us the philosophy is post hoc, so if makes sense, then it can be considered valid and a justification for what you already think is right of no greater or lesser value than any other equally valid justification.