Ladders, Just when I thought I was out.
2 Attachment(s)
Here's a beast that is filled with relational ladders:
Attachment 101 I got this far, but no further: Attachment 100 Anyone see the next logical step? I converted the ladders into inequalities to try and help, but I don't see it. Call the Columns A, B, C and the first row D. I use (+1) and (+2) to mean that the inequality is the same as saying C5 + 1 = C1. I use the inequality sign as a mental reminder of what I'm doing. I use 1 and 2 to indicate increments of position, rather than the actual value of years. A2 < B4 C5 <(+1) C1 C5 <(+1) A3 (At this point, we know that A3 = C1) B1 <(+1) B5 A4 <(+2) C4 Normally, I would pair up these inequalities to see if any of them form logical relationships. However, I get nothing through these pairings except that A3 = C1 
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. 
P.S. I looked harder at your labeling system. I think you see 3 columns, each with a grid, and then you label within that grid. When I look at this puzzle, I see 15 columns and 15 rows, one large grid.
FWIW, I use programming pseudosyntax in notes for myself, with long lines for relationships with a delta on the line, so I might write something like: Redland  250  Arnolds Park+Tyash or 5,000AD+(250500)  250  9,000AD+(500750) Which is way harder to type than to scribble ;) 
That did it! I hate when I miss a fundamental elimination like that.
As for the Xs on the 750 row, here is how I got that: Clue 9 says that Xidat and Quasqueton are 500 years appart. Both have two potential values on the top row. They overlap at 750AD. Thus you could say: "The culture that was founded in 750AD is either Xidat or Quasqueton" Then I look for anything that is neither Xidat nor Quasqueton and mark an X on the 750AD line. As well as the Xidat is not Quasqueton box. Clue 8 has a similar overlapping set at 500AD. I shoot myself in the foot with these puzzles. I look for the hard ones on purpose. In Firefox, I hold down the CTRL key and click the "New Game" link about 1012 times. I then hit CTRLTab to see if one of those tabs has a game below a 30% solve rate. I close all the other tabs. This particular puzzle has a 20.9% solve rate. So only 1 in 5 players stick with it. I didn't want to be one of the 4. ;) 
Thank you for the 750 part, I see how you did that now. :)

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