The problem is that both of your “solutions” destroy the rhyme scheme, and “Spirit” would also spoil the rhythm. There’s absolutely no reason not to use “Holy Ghost”; in its original sense it means exactly the same as Spirit, taken from the German “Geist” which means that. The Germans still use “der Heiliger Geist”, why shouldn’t we English speakers use “Holy Ghost”? I always have, as has everyone I grew up with.

Re: the “I” vs. “we”, the poem is taken from, if I remember correctly, the “Dream of Gerontius”, where the speaker is the Soul preparing for death, so the singular makes sense.

“doggerel”?
there is nothing clumsy or structurally incoherent about using “I”, especially since JH Newman was writing it from his heart to express HIS faith in Christ.

I totally agree with your sentiment. At any one time there are people of true faith and those who have not yet true faith singing this hymn together – I feel these declarations should be a personal declaration to God. Others can do likewise and it’s edifying that we’re actually doing it together.
Yes, “we” is supposed to be a bonding exercise – but it can often be a tribal chant.
To me tribal chants are a thing of this fallen world we see with all the flag-waving and ultra nationalist sentiment which leads to all manner of exclusion

As to the tune, I actually didn’t know this hymn until last year, but Drakes Broughton is the tune that went with it; I haven’t yet found a really decent, fully sung youtube video with it, but it’s a beautiful hymn. I prefer this tune to either of the others I’ve heard with it. To each their own, though; I know there are hymns that have several (“Faith of our Fathers” is another I know at least three tunes for!)