I work as a flight dispatcher, mostly on 737s.
Our system does not work with required distances, but with weights.
Calculating performance for a B739 from GLA using the following data:
RWY 24 INTERSECTION D1 DRY, WIND: CLM, OAT: 15C, QNH: 1013
PACKS: OFF, A/I: OFF, FLAPS: 5, THRUST: FULL
Our program returned with a field length limited weight of 78885kg, a margin of only 2kg on our MTOW (paper derated), on the factored take off requirement.
This in turn means that EDI 24, from D1 is slightly above the minimum needed runway length for a 737-900.
This length is 2553m, however you need to keep in mind that our engines provide 26,000lbs of thrust and the highest rating for the -900 is 27,000lbs.
For reference a -800, rated 24,000lbs thrust with the same conditions gives: 75725kg FLLTOW
a -700, rated 22,000lbs thrust with the same conditions gives: 71958kg FLLTOW
For the -900, with max thrust available the take off run should be below 2500m (though I think the AWS value of 1820m is a bit too low, at least for the 79tn variant)