There is very little that separates the 6.5 PRC and a 270 at hunting ranges. The recoil, like the 270, is between a 308 and 30-06. Your specs point toward a custom rifle, as most of the short-barreled, compact factory rifles are chambered in lighter cartridges. Also, factory rifles for 6.5 PRC tend to have mid-length barrels compared across a set of cartridge offerings. I'm not entirely sure why, perhaps because the thinner calibers prefer a longer barrel to get up to speed and/or velocity (as a function of barrel length) being a very heavily focused selling point of Hornady's cartridges. There are a few factory options though with some overlap:
The Weatherby Camilla has a 13" LOP, if that matters to you more than barrel length (22" without the brake). Would have to go 280 AI or .243 for something similar to 6.5 PRC. Top of your price range for just the rifle.
The Camilla Ultra Lightweight was designed by women, for women. The graceful lines are befitting of the way the stock fits female shooters. FINISH Barrel / Receiver / Brake - Midnight Bronze Cerakote Bolt / Bolt Knob / Trigger Guard / Safety - Graphite Black Cerakote Hand-laid, raised Monte...
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Xbolt SPR has a 13 5/8 LOP with a 20" barrel in 6.5 PRC. Meets your price point with a good scope.
Experience Total Accuracy with the X-Bolt 2 Speed Carbon Fiber SR. Features the new Vari-Tech composite stock with Browning OVIX Camo finish and is adjustable for length of pull, comb height and grip angle for a personalized fit to the rifle. Redesigned receiver and bolt. Lightweight carbon...
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T3x compact comes with a 12.5" LOP and 20" barrel, comes in a few lighter calibers but 308 kills elk and works well in a shorter barrel. Meets your price point with a great scope.
Tikka is able to meet the requirements of modern hunters by combining traditional gunsmith know-how with advanced technology. Choose your own Tikka rifle now!
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If it is 6.5 PRC ballistics you are after, Backfire has done some talky bits on a
20" barreled 6.5 PRC and 24" barreled 6.5 Creed being only 30 fps apart. It's the same idea as a shortened 30-06 shooting as fast as a longer barreled 308. You could flip this though and split the difference for a 22" 6.5 Creed. No animal would know the difference inside normal hunting ranges, and you could be more confident with the lower recoil on the mountain and at the range in a light weight rifle.
That brings up another factory option, a Savage 110 Ultralite, which has adjustable LOP down to 12 3/4. The 22" 6.5 CM option is 5.8 lbs. This could work well for both you and your kid, as you can change the pull length as needed, and the recoil would be more kid-friendly. They also offer a 22" 270, which would have a higher mag capacity than a 6.5 PRC, more reliable feeding from a slimmer cartridge, the same ballistics inside of 500 yards, and a bit more surface area in the expanded slug.
Or get a fancy custom gun for yourself and a standard youth model for your kid..
