As mentioned above, I'm all for you getting exactly what you want, but the rifle you are describing is not going to be any lighter than the Tikka Superlights you can get from Cabelas. Both the McMillan and Manners stocks often end up on the heavier side of what they say they will be, especially once you put a decent recoil pad on them. Or all the ones I've owned are on the heavier side, just as often.
My 2017 Tikka T3X super light (the Cabelas model with the ugly came stock) in 300 win mag weighs 5 pounds 15 ounces with a really nice factory recoil pad and with the big vertical grip they make for it. It's an ugly but great stock, functionally, esp with that big fat grip--lots of palm swell and nice vertical angle. I bought it 2 months ago, I think it was $899 or something. It shoots various factory accubond load into .5MOA to .66 MOA groups. Nearly all the groups it shoots (off a bipod or bench) makes my 1" target dots look very large.
The factory stock weighs 32 ounces WITH magazine, bottom metal, big straight grip, AND that sweet 1" recoil pad. I didn't weigh the stock without bottom metal or magazine but I am guessing this means the weight of the stock without bottom metal and mag is in the 24 ounce range. Same or lighter than a Manners/McMillan. Note that a 1" pachmayr recoil pad adds about 4 ounces to the stated weight of all those ultralight stocks. I shot a 1/2 recoil pad on an ultralight 30-06 for a while...it sucks. Prepare for major collarbone bruising if you shoot it prone very much...esp with a win mag. I just sent that stock back to Manners to get a 1" pad put on.
Bottom line...you might just want to find a Tikka factory ultralight stock or maybe just pick up a TX3 super light. I say this as a guy who has a fair number of custom rifles.