Declined Latin nouns in English prose

Solution 1:

You can still find Jesu, the vocative of Jesus in hymns and probably other liturgical texts (Wiktionary on this). Some examples (all are titles):

• Jesu, joy of man’s desiring
• Jesu, grant me this
• Jesu, good above all other
• Jesu, lover of my soul
• Jesu, thy boundless love to me

Solution 2:

reductionem ad absurdum, using the accusative form of the word reductio when it has the function of the direct object. Are there any (relatively recent) examples of this in English literature?

If you want a quantitative answer regarding 'reductio ad absurdum' then I refer you to Google Books.

Google ngram: reductionem ad absurdum,reductio ad absurdum

You can see that there is not a single instance using the accusative case.

If you want a general answer with regard to all possible Latin expressions then that is a research project. You may wish to try specific ones that you have in mind by using ngram yourself.