I worked it out, but your LetterNumberLadder thing isn't making sense to me. I type fast, so I will type this out.
Going through the clues, my work matched yours except:
I had an X for Lyeilia+9,000, from Clue #2 < this is the key missing element
You had X's for a few things I couldn't figure out how you got, though I didn't need those X's for the solution. It's a bit hard to see through my scribbling, but the X's along the 750AD row (and corresponding 250 years off X's) are what I didn't get.
Using the missing X for Lyeilia+9,000, you find that Lyeilia and Xidat are 6,500AD and 9,500AD, which gives X's for these years for all three other cultures. Neither Lyeilia nor Xidat could be 500AD and one of them has to have had a population of 9,500, thus there is an X at 9,500 and 500AD.
Grid work from there.
