"Fino" is being used here in the unusual and rather archaic sense of "amoroso". "Morir de fino" is to die of love. I've suggested "die of devotion" because I thought the alliteration and the rhythm might suit your version, and also because "fino" specifically implies faithfulness or constancy in love.

"Morir de fino" comes up in a number of old Spanish plays. Moreto uses it a couple of times in the seventeenth century. Here are examples:
http://www.google.es/search?num=100&biw=1024&bih=653&site=we...

The meaning "amoroso, afectuoso" for "fino" is still in the DRAE (definition 5).
http://lema.rae.es/drae/?val=fino

It's there in the first RAE dictionary, dated 1732. It's the third definition of "fino":
"Significa tambien amoroso, segúro, constante y fiél, como amigo fino &c."
This is illustrated by a passage from the play También se ama en el abismo by Salazar y Torres (seventeenth century):
Porque en tan heróico intento,
sepan que muero de fino,
y no de infelice muero."

I can't post a link to this that works, but you can see it (and also subsequent RAE dictionaries) at http://ntlle.rae.es/ntlle/SrvltGUILoginNtlle

So "morir de fino" is a literary set phrase.

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Note added at 59 mins (2013-06-13 09:10:40 GMT)
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In practice you may want to turn it round and say something like

"may I die of devotion
in my loyal suffering",

which is what it means, in effect.