With a brake and that scope, you will probably be under 9 lbs. I have the same chassis, and with the 5 oz folding attachment, 25 oz Bat Vampire action, 2.8 lb 20" Bartlien carbon 30 cal, 11 oz magpul bipod, 28 oz NF NX8 2.5-20 in NF rings, and a Silencerco ASR muzzle brake, I am at 9.7 lbs. My build is the same thing, but a 30 nosler with a silencerco supressor. With the supressor, brake and mag all up will be 10.5-ish lbs, but I will likely take the bipod off when I'm packing on my back vs on a horse, and maybe run it with just the brake and without the folder if weight is a real concern, so can go as light as about 8.8 lbs, pretty sweet to have that versatility.I've considered the 33-28 as well. I have a benchmark carbon 26" sitting here for it. It will be braked. The whole build will be a xlr 4.0 mag w/ carbon butt stock, kelbly nanook, benchmark carbon 26", terminator t3, mark5hd etc. my plan is to finish around 9-9.5 lbs and it will be a a mtn elk rifle. Reason to keep with the 250's is since it will be what I consider to be on the lighter side for long range I want it to be shootable and spot impacts. Especially for people like my small framed wife or on occasion when others use it who may shoot less and not have optimal recoil management.
I think the nanook is a touch lighter, the Bartliens are a little heavy and your bore is .338, so your barrel will probably be close to the same. I would guess you will be in the mid 8 lb range depending on rings and any other additions.
I think for simplicity in your case I would do the 33 nosler, especially with the scarcity of components for forming and such. Just another thing to look into, the 250 Badlands Super Bull dozer gives pretty amazing ballistics in that weight range, I was using it in a .338 Norma with a .417 G7, and it will be alright in a 10 twist or tighter.