Slightly off-threadm but something else that came to mind was putting lyrics from other hymns to the tune to "St. James Infirmary."
One that works is "I Stand Amazed", though you have to add a syllable to first line.

[Now] I stand amazed in the presence
Of Jesus the Nazarene
And wonder how He could love me,
A sinner, condemned, unclean.

Another that would work is "Redeemed"

Redeemed, how I love to proclaim it.
Redeemed by the blood of the lamb.
Redeemed through His infinite mercy
His child, and forever, I am.

There are, no doubt, many others that would work as well.