All but one of the following sentences incorrectly sacrifices logic for the sake of consistency of verb tenses; revise verb tense forms as necessary.
1. Working with such close friends as these three were could have been problematic.
2. My visit to Yellowstone National Park was the most enjoyable vacation I’ve ever had.
3. She didn’t even know that Tuvan throat singing existed.
4. He was especially interested in how binaural recording worked.
5. They wanted to know how the policy benefited the company.
Solutions
When a continuous phenomenon is discussed in a sentence framed in the past tense, the phenomenon should nevertheless be described in the present tense.
1.
Original: Working with such close friends as these three were could have been problematic.
Correct : Working with such close friends as these three are could have been problematic.
Presuming that the people referred to are still friends, the linking verb should be in the present tense.
2.
Original: My visit to Yellowstone National Park was the most enjoyable vacation I’ve ever had.
Correct : My visit to Yellowstone National Park is the most enjoyable vacation I’ve ever had.
Even though the visit is in the past, it is still, as explicitly stated in the sentence, the person’s most enjoyable vacation, so the linking verb should be is.
3.
Original: She didn’t even know that Tuvan throat singing existed.
Correct : She didn’t even know that Tuvan throat singing exists.
Tuvan throat singing is extant, so the final verb should be in the present tense.
4.
Original: He was especially interested in how binaural recording worked.
Correct : He was especially interested in how binaural recording works.
The technology described still works, so the verb after that phrase should be works.
5.
Original: They wanted to know how the policy benefited the company.
Correct : They wanted to know how the policy benefited the company.
Sometimes, whether a verb should be in the present tense or the past tense depends on the context. In this case, if the policy still benefits the company, the final verb in this sentence should be benefits. If the benefit was temporary, the sentence is correct as is.
Not sure of solution n. 2
What about, “My visit to Yellowstone National Park has been the most enjoyable vacation I’ve ever had.”?
According to Fowler (2nd ed.), what you describe as correct is abnormal. It is referred to as “vivid sequence.” Normal sequence of tenses is to maintain the tense of the initial verb. “He explained what relativity meant” is proper. “He explained what relativity means” is, I think, what you recommend. It is correct as an alternate, but generally less favored than keeping the tenses synchronized.
I was taught that vivid sequence was incorrect. I stand corrected. But normal sequence of tenses is certainly not incorrect.