To my understanding all particles affect the word or clause that appears before them: 「駅から家まで行く。」 means "I'll go from the station to my house" rather than "I'll go the station from house to go". So if this logic applies, shouldn't it also be true for 「から」 and 「ので」? 「私は忙しいから行けません。」 To my understanding, here 「から」 is connected to the first clause and not to the second one. So the sentence is worded similarly to: "because I'm busy, I can't go." When Japanese doesn't need a comma between the clauses because they're already connected together by 「から」. If it was connected to the second clause instead of the first one it's meaning would become more of a "so". Also the literal meaning of "from" for 「から」 and "in of" for 「ので」 is much closer to "because" than "so". Is my understanding correct?
It is your choice what to want to keeep and what you want to lose when you translate from one language to another.
If you seek an English equivalent of ので, you cannot preserve both the ordering of clauses and the position of pauses.
If you privilege the ordering of clauses, than "so" or "therefore" will be preferrable, because they come after the causal clause, and before the statement of its consequence.
The price for this, though, is that you have to pause before the conjunctive particle, as is not done in Japanese. Moreover, you lose the hierarchy of the sentence structure by turning hypotaxis into parataxis.
If you privilege the position of pauses instead, and if you want to keep clause subordination as such, you should use "because", "since", which cluster with the causal clause as ので does. This way you are also preserving the hypotactic structure.
Same with から、and with a lot of Japanese particles. For example のに, which has a concessive meaning but structurally works in the same way, and can prompt similar doubts as to whether you should translate it with "but" or "although".