hi @langostein thanks for dropping by. those you mentioned are already in my list. especially the "who" and "whom". you are exactly right when you say people misuse words. but who can blame them English is a crazy, brilliant, weird, versatile language. Hoping this series will clarify these ambiguities.
I am no guru in writing but I appreciate you shooting at me some concerns about your own writing. Both sentences you referred to, IMHO, are well constructed and by including the word "that" in your sentence, you are simply "emphasizing" and "limiting the scope" of the point you are making within the two things THAT you struggled with. I hope this helps. Again, I don't claim this to be accurate or correct but we have many good writers here in Steemit and hoping they see your concern and jump right in to give their expert opinion.
About the word "that", consider the following sentence:
"He gave me an answer but I know that that is not the right one."
Just something for you to ponder. ;-) Have a good one, today!
I appreciate your response.