Mine is also right around this weight, although its a short PL action. Barnard did a run of the larger PL actions, but kept the length the same as the P (which is 15mm shorter than the PL in "normal" configuration).
So I reckon you could work on an action weight of say 1,100g, plus a stock at 1,000g (incl bedding) to then work out your barrel profile. A Game Scout stock is lighter again (750g) than an A5, and an A3 sits between the 2 if taking more weight out is a priority. I think its Pacnor that have a handy barrel weight calculator on their website that would be useful for giving you an idea of barrel weight.
Also, have you looked at other action options? You can get a short action Hardy with a Mag bolt face (or Lapua Mag) with a solid bottom, so set up as a single shot. My brother has one sitting in a box for a build like this.
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