Guessing it's a magazine cut action so your best bet would be a hawkins hunter bottom metal with the flush long action mag. Downside is cost, that combo is probably 325ish... upside is that it will be compatible hardware with most stocks available with a m5 cut. Still a bit heavier than a straight bdl but a good option to keep the door open for big mags at the range.
*edit; figure it's worth putting out there it's probably a good idea to temper expectation of how light it's gonna get. The bergara rifles always seem to land heavy, the stock is only at best half the problem. The actions are a little husky and they definitely skew towards the chunkier side of barrel tapers and contours. Not saying it won't get noticeably lighter with a stock swap and some svelte dbm. That's a heavy stock, but it's also # 6 contour barrel. Would a manners uc save the most weight... absolutely, but dollars would probably be best served shooting for moderate gains and a curb weight Un scoped around just shy of 8.5. I've handled the adjustable hmr rimfire stock, even the mid tier options would save a pound off of that thing. Lightest carbon in the world with adl, it's still not gonna be a kimber montana. But hey a pound is not nothing on a shoulder.
