Story Mode:

9:30 by JayFermont on 12/29/12 (from SRL, probably wrong) http://www.speedrunslive.com/races/result/#!/31595

8:28 by JayFermont on 12/29/12 (from SRL, probably wrong) http://www.speedrunslive.com/races/result/#!/31597 ... 7:19 by Vulzi (?)

7:16.42 by Vulzi on 10/23/13

(More vulzi?)

7:08.61 by Yvathacal ... 6:55.90 by Yvathacal

6:51.91 by Icebound777 on 1/21/14

6:50.72 by Icebound777 on 1/24/14

6:48.83 by Icebound777 on 2/4/14

6:48.05 by Icebound777 on 2/13/14

6:47.91 by Icebound777 on 3/9/14

6:45.15 by Icebound777 (?)

6:42.98 by Icebound777 on 4/15/14

6:42.12 by Icebound777 (?)

6:42.09 by Icebound777 on 4/28/2014

6:41.81 by Icebound777 on 6/30/14

6:40.36 by Icebound777 on 7/10/14

6:39.30 by Icebound777 on 9/2/14

6:38.64 by CyclopsDragon on 2/5/15

6:38.51 by Andreww4 on 7/27/15

It's a shame the nrush spreadsheet appears to have lost all its revision history :(

I managed to find a few bits (mostly 7:20 - 7:00 runs) missing above from my IRC history (#nrush on SRL), but bombch.us seems a little broken right now (at least for me) so I don't know if the links will ever work:

Time & link: 7:18.12 by Yvathacal - http://bombch.us/NZS 2013-10-20 (start of channel, so I don't know what date that run was actually on)

Time & link: 7:16.70 by Yvathacal - http://bombch.us/OEl 2013-10-29

Date & Link: 7:08.61 by Yvathacal - http://bombch.us/OZf 2013-11-02

Time & link: 7:07.90 by Yvathacal - http://bombch.us/PQS 2013-11-11

Time & link: 7:07.37 by Yvathacal - http://bombch.us/Qby 2013-11-25

Time & link: 7:04.69 by Yvathacal - http://bombch.us/UAV 2014-01-05

Link: 6:55.90 by Yvathacal - http://bombch.us/VHO 2014-01-13