Does 再见 work for "goodbye forever"?
Does 再见 imply you will meet again, as the literal meaning suggests?


Yes 再 = again; 见= see; 再见 = (see again) goodbye


  荆轲正在和朋友们说再见。“风很大啊水很冷，勇敢的人去了，永不再回！” Which literally says, "He was saying "see you again". 


In this third person narrative, the narrator translated the classical term '告别'(announce departure = say goodbye) to a modern term '说再见' 

It is not too big a problem, because even 荆轲 really said 再见了 instead of 别了, that just meant he didn't want to state the obvious and pretended it was a normal goodbye

永不(never) + 再回 (return again) = 永不再回 (never return again)


  Does 再见 work for “goodbye forever”?


No, if you say 再见 to someone, it means you are expecting to see that person again. Although you can always pretend it is not a final goodbye and say 再见 like it is a normal goodbye.


To say 'goodbye forever' you have to state it clearly, like: "我们永远不会再见了" (we will never meet again)
You can also use '永别了' (apart forever = goodbye forever)


'永别' means '永远分别' (forever apart)