It seems to me that you are right that it means "so as to" or "in order to".
There is some support for this in the Oxford English Dictionary, under "so" 28.a.
so..., or so...as, so as, followed by an infinitive denoting result or consequence. The omission of as is now regarded as irregular.
By "so as", the OED means what we often call "so as to"; it regards it instead as "so as" followed by the full infinitive. Similarly, so... here is a reference to "so" followed by the full infinitive, i.e. "so ... to ...".
1709 J.Swift: He has been indeed so wise, to make no Objection against the Truth of my Predictions.
Today we would say "...so wise as to...".
However, you may object that "so + adj + to" is a different kettle of fish from "so to". The OED has citations here for "so as to" and "so adj to" but not for "so to". On the other hand the editors viewed the senses as sufficiently closely related to group them all under 28.a.
The most recent citation even for "so as to" is, at the time of writing, from the 19th century (the entry hasn't been fully updated since it was written in 1913 - I imagine that when the staff finally get to this, they will have access to a lot more information than was easily available back then).
1896 Law Times 100 488/1 To repair the drain so as to abate the nuisance complained of.
Regardless, it is difficult to see how "so to" could mean anything other than "so as to" in the Shelley quote.
Once again arose the voice of praise; and then followed an exhortation, full of affectionate earnestness, urging upon the disciples of Christ the duty and the privilege of striving so to enter into sympathy with Him in his agony . . .
It is a bit harder to be certain but I think that this too means "so as to": in other words, that Christ's disciples are being urged to strive to enter into "sympathy with Him in his agony". I don't quite understand this well enough to paraphrase, but that may be due to limited understanding of the relevant theology on my part.
The most obvious alternative interpretation would be to take "so" as a pure adverb (=in such a way), but "to" on its own would seem to carry much of the same meaning as "in order to" in this context, so I think the sentence would end up meaning much the same thing.