Only flaw I can find in your Armory is that you're not using TV glyph. With Exo now proccing it as well, there is absolutely no reason to never have TV glyphed. Trinks are fine, though, for now. You are hurting by not having a Feather - but the "Fabled" portion of its name is hilariously accurate. I also wouldn't sweat it too much as the thing is getting nerfed directly next patch, on top of the RPPM nerf.
As for the logs, it looks like you have some serious rotational issues. Looking solely at Consorts, a 7.75min kill, WoL shows you had a total of 4 ES uses in almost 8mins - half of what you should have...Five ES casts, sorry, looks like you used it once to heal. With having not died, there's really no excuse for so many wasted potential ES casts. Then there's Inq, which you've cast 20 times over the fight where you should really have only cast it 15~16 times. It's not a huge problem, but it is still wasted HoPo that you have to rebuild.
And, looking at the Full Report, in a three hour raid period, it looks like you used SS exactly once. That means you're being a burden on your healers by not doing everything possible to avoid/mitigate damage (kinda goes hand-in-hand with the TV glyph thing). I also notice a lack of Hand spells used, though that's not really a big deal in a 25-man where most of the need for that utility is covered by more people.
Now, as to the Warrior, I know very little of Arms, but he's not exactly got his gear in the best shape it can be - and I'm mostly contributing that opinion to his reforging. He's got more than 1.5% excess hit, and his Zerat is untouched. Looking at all the crafted gear and his achieves, I'm'na assume he hit 90 just a couple days ago? He's got one full-clear of MSV LFR, which means zero progress on the legendary questline - and that cloak is gonna be a huge boon once it actually turns orange.
Honestly, I think it would hurt your guild's 10-man aspirations more to bring the Warrior. What buff are they trying to extract from him - Skull Banner? It's a nice buff, but it's not a make-or-break kind of thing unless the group is stacking crit-heavy specs. Say the same of Battle Shout, unless the raid is physical-heavy. The health shout can be nice, but so's Devo Aura. Warriors don't really bring much beyond that and raw damage, but he's sorely lacking in gear which hurts his damage.
Focus on better managing your rotation (look into ClCRet if you have to) and the Paladin's array of utility, possibly try Selfless Healer. SH has been quite the boon for me and my raid group in allowing me to fake the addition of a fourth healer in certain situations.