Eying or Eyeing?

Both words 'eyeing' and 'eying' are accepted by dictionary.com and Microsoft Word, however here it says that eyeing is wrong. Interesting. As with most things, I hate not having a definite answer. It messes me up. How can I write my story with two ways to spell the same word? I don't mind two synonyms, but that's different than two spellings. Oh, right, forgot to mention my story. I'm writing a Star Wars themed "choose your own adventure" story, which coincidently has a ton of different choices that affect the course of the story. However, choices are only good if they clearly have two different outcomes. Having one word that by choice can be spelled two different ways is driving me insane. Maybe it's just me...