I opened up Barnabas, and 1:1 is like, "whoo this is easy", and then 1:2 is like "errr, what on earth language is this".

I think you are likely selling yourself a bit short here. I would venture to say that in verse 2 the biggest hurdle you are having is vocabulary, but what do I know, right?
These are some of my observations when reading the Church Fathers, but I don't presume that my limited readings are representative of the difficulties you might encounter in the corpus:
1) Depending upon the author, you are likely to encounter Greek forms and usages that you don't see as often in the New Testament. Personally, the items that gave me the most trouble in no particular order were: 1) More frequent use of the optative. 2) More varied use of infinitives. (I have mentioned this last issue quite often on the forum, and I am glad to say this is not nearly the ordeal it once was.) 3) More varied usage of conditionals.
2) On occasion, I have noticed the Fathers quote or allude to other other ancient authors (I have Plato in mind specifically, but there are others. He stands out because I am more familiar with his writings.) There have been times in my readings when understanding the allusion/quote will make or break my understanding of the text, even if I otherwise have the sense of the passage.
3) Learn the vocabulary of a passage before you attempt it. Other than taking the time to work through an Attic Grammar (well, technically, one and a quarter), this has been the single most helpful change that I have made in my own private readings. Skim the passage, jot down the terms you don't know, consult a lexicon, and memorize the definitions, lexical forms, and/or principle parts. Don't start the text until you are confident you know the vocabulary. This has helped me more than I can say.
4) Don't quit.
Good luck!