I understand you are trying to get this to your anniversary. 2 thoughts.
1. Why not make the number 6142003? You might be able to hit that without adding the silly .1603 (which is the part I don't like) - oh i did this in excel and you'd need to integrate x from 1 to 200 and y from 1 to 167.8858. Obviously you could find some different numbers, I just did one quickly.
2. I don't want to be cheesy or anything, but what if you changed it like this. Instead of x+y, use a+b and write assume a=1 and b=1 under the problem. (I was thinking why not 1+1, but I assumed you were trying to make a reference that you and your wife were different people, so that's why I went with a+b and I always found it funny when you "assume" stuff in math classes.) You can still double integrate over x and y. Then use x from 0 to 25 and y from 1 to 15.28401. You could change the 25 to your age when you met (thus you were alone from 0 to that age) and change 1 to the length of your engagement. Then just use the goal seek function to find the top bound. You could make up a cool story about that number as well, but I didn't see any other way to get to 614.2003.
If I had some duct tape, I could fix that.