Learn English – “I’m having” – an illness

The relevant distinction between the two participial adjuncts is in the specification of aspect. Having come this far... is marked for perfect aspect. The perfect is used to indicate an event having occurred prior to some reference time (whether this reference time is at the time of speaking, or at some focal point in the past or future) as having continuing relevance. Perfect aspect is marked in English with the auxiliary verb have.

The other adjunct, Coming this far..., is not marked for aspect, so there is no grammatical indication as to whether the event is complete, ongoing, or yet to be undertaken. The default interpretation is that the event is ongoing when you use present participle adjunct without perfect marking.

In deciding which sentence is best you need to consider the functional motivation in choosing to use perfect aspect versus leaving the aspect unspecified. If you want your adjunct to point out a past event with continuing relevance to the main event you are describing, the perfect aspect is preferred. If you want to refer to an event, but its temporal relation to the main event you are describing is not too important, then you don't use the perfect.

The first choice is preferred because the fact that the delegates have already "come far" is relevant to their feeling of wanting to accomplish at least something. The aspectually unmarked adjunct would be preferable in the case where the main event was somehow framed by the event depicted in the adjunct. e.g.,

Coming this far, the delegates made many friendships and alliances amongst themselves.

I think "bigger" might sound better because size is more suited to relative adjectives. It also perhaps better matches the sense of gradual change in the sentence.

We can see the shrine become bigger, little by little, from the ferry.

... sounds fine to me. Whether to use "become" or "becoming" doesn't seem an issue of correctness.