Well if that's the case then the 280mm should work. It's about 21 inches from the center of the BB to the top of the seat post clamp, and then I need another 7 inches from there to the seat rails. 7 inches is approximately 180mm, leaving 100mm or about 4 inches into the frame. That's a little over an inch below the top tube. So it should work, but I'm still wondering if I should play it safe and go with a 350mm post.

I could make this easy on myself and find out what the minimum insertion length is for both of the posts I'm looking at. I'll have to search Google images to see if I can find anything.