Unfortunately the 'movie' is inconclusive and just seems a collation of various sources and uses standard references, which, in our culture misses the whole point of the inner spiritual reality of the myth. Wiki isnt going to lead to understanding the myth or the card.
Hercules actually fights and kills his totem ... he doesnt cross the mountain he smashes through it ... and so on.
The is the path of the denying ego and and relates more to a rampant Mars. It is not the strength of a woman holding a lions mouth open ...
Hercules path is one of failure during the initiation process , one only has to see how the story ends for him. He isnt admitted to the mysteries ( they did form an 'outer court' or lesser mysteries specifically for him ... and his ilk ).
Yes, he did make it to 'heaven' ( as a constellation) and there he is up there .... still battling away and fighting the cosmos
Perhaps if someone ever invents two sided tarot cards *, he could be on the reverse side of Strength.
* patent pending