I love brine/soleseife bars. I use a "regular" recipe (eg, one of my "basic" recipes that I used w/the last brine bar: 63% lard, 20% coconut, 10% olive, 7% castor, 7% superfat) and add 25% of the volume of the *water* (not oil) amount in salt to the water, which I heat so that the salt completely dissolves, and let it cool before I add the lye. I don't exceed that salt amount, as I read somewhere that there would be problems with oversaturation/non-dissolving above it.
I also add 3% sodium lactate, a TB of 50/50 sugar solution ppo and ETDA - I have hard water - and between those things (all of which are supposed to help with bubbles a bit) my lather is fine despite the high salt amount and keeping the coconut fairly low for a high salt bar.
After that, I proceed as usual. I usually CPOP, and do with this as well, but keep an eye on it b/c it sometimes (a) gets pretty hot and (b) it hardens fast, so you would generally want to unmold/cut sooner than usual. I do love these bars, plenty of time to swirl, they are hard, quick to set up, v. moisturizing, good lather.
ETA: not sure about the milk, though, sorry.