After reading everyone's responses, I've decided to include the others/white walkers. With that being said, here are the options for how I should go about it. Feel free to add any more suggestions or what have you.
Scenario #1: The Others invade around the same time they are supposed to in canon/when they come in the show, so around 305AC
Scenario #2: The Others' invasion is slowed and pushed back to when Alaric is around 40ish years old, so about 320AC or so.
Scenario #3: The invasion occurs following Alaric's death. I won't give an exact date as I haven't determined at what age he will die, but yeah.
Scenario #4: You guys give me some more suggestions you might want to see, and if someone made a suggestion you like, like their comment, so I can tell.