Choosing a random 7+ minute attempt and zooming in on phase one, since it's a good Patchwerk simulation:
World of Logs - Real Time Raid Analysis
You're doing around 10.3k DPS, which should be a little over 50k TPS with the new threat modifier (5x). It would be around 30k TPS with the old threat modifier (3x). There's no way you could be generating only 15k steady-state TPS with 10k DPS.
Your DK friend is putting out about 3.5k DPS more than you (13.7k total DPS), which should be 68.5k TPS (5x).
So you shouldn't be very far behind him. Your lower DPS can probably be attributed to ability usage. In that 134-second section, you should have been able to cast as many as ~44 Crusader Strikes, but you only cast 30. That's an average of around 4.5 seconds between Crusader Strikes, which is pretty long even assuming pushback from some SotR misses. You may want to try tightening up your rotation, that should help push you down closer to 3 seconds + double latency between CS's.
Some other errors show up when you scrutinize a filtered version of the combat log:
-You seemed to be a little unreliable with fillers. Your first Judgement was at 8:11, the next one isn't until 8:39, almost 30 seconds later. There were quite a few empty GCDs in there that could have fit a Judgement (or Consecration or Holy Wrath). In that period, you should have been able to get off another 2 Judgements.
-Your holy power usage is a little inefficient (slightly more clearly filtered log). You generated 4 Holy Power before the first SotR, but you cast an additional 3 Crusader Strikes before using SotR:
You do this a couple times in the log, where you cast an extra CS when you already have 3 Holy Power before using them in a SotR. In addition, you cast SotR once with 2 Holy Power. Improving your Holy Power efficiency would help considerably.
[21:08:09.552] Risspal casts Crusader Strike on Ragnaros
[21:08:09.671] Risspal gains 1 holy power from Risspal's Crusader Strike
[21:08:13.209] Risspal casts Crusader Strike on Ragnaros
[21:08:13.332] Risspal gains 1 holy power from Risspal's Crusader Strike
[21:08:16.527] Risspal casts Crusader Strike on Ragnaros
[21:08:16.596] Risspal gains 1 holy power from Risspal's Crusader Strike
[21:08:18.693] Risspal casts Grand Crusader
[21:08:18.748] Risspal gains 1 holy power from Risspal's Grand Crusader
[21:08:20.201] Risspal casts Crusader Strike on Ragnaros
[21:08:23.597] Risspal casts Crusader Strike on Ragnaros
[21:08:27.140] Risspal casts Crusader Strike on Ragnaros
[21:08:33.015] Risspal casts Shield of the Righteous on Ragnaros
Cleaning up those two problems and tightening your rotation should help catch you up to your co-tank. Consider that if you were able to shave that CS interval from 4.5s. to 3.5s, that would be a ~28% increase in ability usage, which would be a pretty significant chunk of DPS.