I agree with your post, Alec, except that to your "So really, you're fine no matter what you use" -- I must add "as long as you're consistent in your spelling of the word." ;)

I like this article's response to the question of how to spell resume: http://www.writeworks.biz/newsletter/archives/mythtaken/022003.htm
which gives the basis for each common version, and the best rule of thumb: be consistent or be wrong for sure!