From the mad alchemist :
Dont mash your roasted-and-kilned grains (e.g. chocolate and black malts). Roasted grains will drive the pH down considerably, so its difficult to keep the pH high no matter what fancy solution you use during the mash. Roasted grains have the wonderful benefit of not needing to be mashed. So, the best solution, in my opinion, is to mash everything except for your roasted grains in your MLT, and steep your roasted grains in a separate vessel (below 170 F) simultaneously at around 2 quarts per pound. Then, combine the wort created by the roasted grains with the mashed wort in the brew kettle.
If you dont want to steep the grains, you can essentially brew a coffee with the dark grains with either a more traditional method (heat) or you can cold brew it overnight to really avoid the astringency as much as possible
itll just take longer. If you cold brew, you should probably bring the temperature of the concoction to 170 F after removing the grain to pasteurize it.
Then, you can add the coffee-like brew whenever you want (start of the boil, end of the boil, directly in the fermentation vessel, even just before bottling). All will impart different character, so experiment!
Note that you might not get full extraction from all roasted grains when steeping. According to some experiments run by John Palmer, it looks like Black Patent and Roasted Barley are some of the only roasted malts that have the same yield as mashing when steeped. As such, you might only exclude those from your sweet stout mash, or you can increase the amount of other grains accordingly (e.g. multiply the ounces of Chocolate Malt you use by ~1.5-1.6 to make up for the difference).
I would not recommend sparging with the roasted wort, in part because youre going to impact the sparge pH pretty significantly, and in part because youre going to leave some of your flavors behind.
Hitting the ideal concentrations of all ions in the brewing water as well as the ideal pH is very easy when you leave out your roasted malts (and any other malts that dont need to be mashed, such as caramel/crystal). By steeping the roasted malts (and, optionally, your crystal malts) separate from the mash, you might end up with a much better sweet stout in the end. As someone commented, you could also steep the grains in a bag while you transfer to the boil kettle from your MLT, which sounds like a great idea.