It would be easier to understand the topic if right now I weren't so pressed for time
Were it not for the fact that I am very pressed for time, it would be easier to understand the topic
(If I were not pressed / Were I not pressed ...)
If I took the day off tomorrow and continued ruminating, I might suddenly see things clearly
Were it not for the fact that I won't take the day off tomorrow, ...
(If I were to take / Were I to take the day off tomorrow...)
If I had been born in an English-speaking country, I might never have had this doubt
Were it not for the fact that I was not born in an English-speaking country,...(Had I been born / If I had been born,....)
I wouldn't be thinking about this if I hadn't seen a strange sentence some days ago
Were it not for the fact that I saw a strange sentence some days ago, I wouldn't be...
(Had I not seen / If I hadn't seen.... )
I might have gone crazy some days ago if I were not a calm person
Were it not for the fact that I am a calm person, I might have gone crazy some days ago
(Were I not a calm person / If I weren't a calm person....)
If had to give a class about this topic tomorrow, I would have stayed up all night long yesterday
Were it not for the fact that I will not give a class tomorrow, I would have stayed up....
(Were I to give a class about this topic tomorrow / If I were to give a class...)
For some reason I can't put my finger on, the inverted were-construction doesn't work in sentences such as:
If I had seen it with my own eyes, I wouldn't have believed it
(Had I seen it with my own eyes, ...)
... Maybe the reason it doesn't work is that the if-clause is of the "even-if" type...
Even if I had done more extensive research yesterday,
I might not have been able to clarify everything and I could still have the same doubts today
(Had I done more extensive research yesterday, I might still...)
Going back to the perfect infinitive possibility, quick Google searches return countless examples of "were I to have done", "were something to have happened", and so on. Still, the Internet is not always a source of good English; also, something in the construction seems rather odd to me.
I'm really not sure my understanding is right. Some parts seem to be missing, and there may well be other important considerations I'm failing to take into account. I guess I need to do more thinking!