Per force / perforce

(1) "We could only envy those few French, Canadian, and British nationals of our acquaintance who had managed?per force of their country’s early diplomatic recognition of Mao’s government?to penetrate the Chinese veil."

(2) "Amateurs, perforce, have to settle for less expensive solutions."

(3) "We must, perforce, deal with this issue immediately, as procrastination is not an option."

Most usages I have seen of the word 'perform' use it to express the sense of "necessarily," "without any option," "with a choice" etc., as in examples (2) and (3). But I have recently come across example (1) where the word (note that the author wrote 'per force,' not 'perforce' - I am not 100% sure if the two are the same or if it's a typo) means more like "as a result of" or "flowing from" (i.e. without the sense of necessity or inevitability that is associated with the usages in example (2) and (3)).

Question: what is your opinion on how the word should be used and how do you reconcile the usages in the above examples?

I am very aware that the word is rarely used these days except in rather formal writings. I want to learn its proper usage nonetheless.

Thank you.