I think you need to be more specific when you say, "mountaineering." What exactly are you planning on doing ... technical climbing on rock and/or ice? Glacier travel to volcanic routes? You've listed the Gamma LT and the Proton LT. They are two completely different jackets.
The Gamma LT is a traditional, uninsulated softshell hooded jacket. It is very durable, stretchy and comfortable with an amazing hood that will accommodate a climbing & ski helmet with ease. The Gamma LT Hoody will breath pretty well and offer you decent wind/weather protection. Nothing cutting edge here, but sometimes that's exactly what a mission calls for.
The Proton LT Hoody is not a traditional softshell jacket, even though I think I've read somewhere Arc'teryx may refer to it as such. The Proton LT Hoody has a light, nylon face fabric that is wind and weather resistant. The Proton LT Hoody is filled with 65 g/m2 of CoreLoft Continuous synthetic insulation. CoreLoft Continuous is Arc'teryx's entry into the breathable insulation game; competing with Patagonia's FullRange active insulation, Polartec's Alpha insulation and other offerings from PrimaLoft.
I own the Gamma LT Hoody and the Proton LT Hoody. I don't wear both combined as the Proton LT Hoody was designed to be worn on its own. It is wind/weather resistant enough on its own that it doesn't really work very well as a midlayer all the time. If wind/snow/weather are too much, then a lightweight hardshell, like an Alpha FL, Westcomb Shift LT Hoody, etc. should be worn. Keep in mind, a lightweight hardshell will weigh a lot less and be a lot more packable than the Gamma LT Hoody. Even though "LT" is in the title, it's nowhere near as lightweight or packable as a hardshell.
I've found that the Proton LT Hoody does very well on its own and I rarely, if ever, have to couple it with a hardshell, even though I always have my Alpha FL in my pack. The Proton LT Hoody blocks most wind/precipitation and dries reasonably fast. If you're looking for a synthetic midlayer with active insulation, I also recommend Patagonia's Nano-Air series. I have the Nano-Air Light Hoody and the original Nano-Air Jacket. I find the face fabric the Nano-Air breathes better than the Proton LT Hoody, but isn't as wind/weather resistant, which makes it a better midlayer under a softshell/hardshell when you'll be wearing the shell all day. Keep in mind though, all these active insulation pieces were really designed to be worn on their own so they can breath as intended. The Nano-Air series dries faster than the Proton series in my experience.
On that note, your layering system sounds like a bit much, unless you run very cold. A thin baselayer & fleece layer, coupled with an active insulation piece and a softshell or hardshell is a lot, unless you run super, super cold. Odds are, you'll overheat three minutes into the approach. With a little more information on what "mountaineering" really means, I can help recommend a layering system with the aforementioned apparel.