There is something to be said for taking your lumps and moving on. I figure you win some and you lose some. You just have to hope you win more than you lose. Like the stock market - or poker!
What about sending it to NCS and having them try to "clean" it, having them send to NGC for a re-grade will this count as a cleaned coin or will it re-grade? I know this sounds like going out of the way, but I really do like the coin is absolutely flawless in person, even with the fingerprint.
The fingerprint could definitely have its visual impact reduced, but a ghost of a print it likely to remain and it may, over time, start to become a bit more obvious. You must really love this coin because the expenses you are considering are a tremendous percentage of the coin's value.