As a Paladin healer up top about the only recommendation I can make for mana management is to use your Potion of Concentration when you fall back down at some point because while she is casting Smoldering Devatastation there should be the least overall damage going out. Likewise you'd want to time Mana Tide for when all healers are on the bottom if you had one, sadly you don't. The big point I always try to drive home on an add management encounter like this is sticking to your priorities. DPS may feel the urge to improvise a little however provided each part of the machine is doing its job then the greater goal gets accomplished.
I'd still recommend only sending two DPS once, one the second time, and none the third in order to make sure adds are being handled. Course it isn't my raid to lead. Also without logs it is hard to see where any specific breaking points would be.
As far as throughput is concerned, my guess would be that half or more of the weapons in your raid could be replaced by 365 crafted ones, you yourself have already done so but the rest probably haven't. In my raid litterally the first raid night of the week where those patterns were first available I handed out 10 new weapons for 8 people (2 of the people including myself already had 378 weapons). This was a very easy way for me to directly impact the actual throughput of the raid and all I had to do was sacrifice a small portion of that massive surplus of liquid assets that were built up from selling unused T11 BoEs for the past five months. Simply going out and getting new weapons for people if you have the assets to afford it is a very easy way to help your raid in just starting new content.
"In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.