A lot depends on how much you think the Model 12 Competition action adds to the package and its performance. It has a larger diameter receiver than the other Savage 12 actions, and much smaller ejection port which is more on the side than the top, both adding stiffness. The larger diameter also sees a heavier / meatier barrel in the chamber section used. There are three bedding screws instead of two. All Target Action models have the competition version of the AccuTrigger that adjusts down to 1/2lb pull-weight. The target action might not add much if anything other than the improved trigger initially to your shooting at this range, but gives you a superior action as the basis for any future rebuild as a custom or semi-custom rifle. Over here on our side of the Atlantic, Target action models hold their secondhand value much better than any of the sporting models, and that probably applies with you as well.
If you want a cheaper model with this action, or simply the basis of a very good gun, I'd recommend the single-shot version of the 12 LRPV (right bolt; left port) with heavy 26" barrel as an alternative to the Target Series rifles. I'd also class the LRPV as preferable to the BVSS for your shooting, unless you really prefer a laminated stock over a synthetic one. The LRPV has a really good HS Precision stock with one of the longest, stiffest moulded-in bedding blocks you'll find - better than the Remington 700 Police and similar models, and a very stiff synthetic stock. (The BVSS and F/TR etc with laminated stocks are pillar-bedded, but with very small pillars and usually benefit from a bit of work on the bedding.)
The .223 Rem LRPV is available in 1-7" or 1-9" rifling twist rates, and I imagine the former will also be throated longer too. 1-7" lets you use all the 80gn bullets available on the market, which buck the wind a bit better than the 69-75s that the 1-9" twist handles, and can provide superb accuracy. It also handles the new 90gn models, the Berger VLD and Match BT Long-Range the ones to try. At 26" barrel length you don't lose very much velocity over 30" with the little .223 Rem cartridge, not enough anyway to worry about at 300 yards. You'll still be able to get 2,900 fps or therabouts from an 80-grainer.
I know from personal experience how well the 12 LRPV package works having won last years UK Benchrest Assoc 'Factory Sporter' class championship with one chambered for .204 Ruger. I've also seen .223 Rem versions perform very well off the bench at 100 yards, albeit all those I've seen so far in this chambering are 1-9" twist models, which is almost certainly a better choice than the 1-7" for this range.
Something else for you to consider anyway!
Laurie,
York, England