16" barrel/caliber combo for 1K yards

Here is another data point for ya; I've got an 18 inch 6.5prc bartlein barreled tikka that goes about 2775 with factory 147eldm ammo. At my elevation, that bullet drops to 1800fps at around 950 yards. To go down to 16.5 inches would likely take off another 50fps.
This is a fine example.
Pushing the same bullet as a 24" 6.5CM, but with a 6" shorter barrel. This makes sense for a deer rifle.

I have a 20" 6.5SS that pushes 156 Elite handloads at 2916fps. Those numbers equate to about 1100 yards to retain 1800fps & 1000ft/lbs on target @ 6500' and 30°.
 
A ballistics calculator will need to become your new best friend. Most likely you will have to focus on big magnum speeds (think 300 RUM or Norma over the 300 WM or PRC) for the 30 cal. and high BC bullets. Same for 7mm or 338 calibers. I wouldn't look at anything lower than 7mm if it is possible that elk might be on the menu. Increasing your barrel length from 16" to 18" should be an easy compromise if you want to hit your parameter. Muzzle blast with a brake on 16-18" barrel with big magnum power will be substantial.
 
This is a fine example.
Pushing the same bullet as a 24" 6.5CM, but with a 6" shorter barrel. This makes sense for a deer rifle.

I have a 20" 6.5SS that pushes 156 Elite handloads at 2916fps. Those numbers equate to about 1100 yards to retain 1800fps & 1000ft/lbs on target @ 6500' and 30°.
Factory 143 and 147gr out of my 24 inch factory length tikka 6.5 creedmoor barrel is closer to 2650fps. A solid 125fps slower than the 6.5prc with 6 inches less barrel. Loaded hot with handloads, I have little doubt the PRC would gain another 75-100fps if one wanted to.
 
Per your specs of:
16" barrel with a brake,
800-1000 yds,
enough energy for deer at 1000yds.

You're going to need something with a lot of powder and heavy bullets. The muzzle blast from something like that with a 16" barrel w/brake is going to be crazy. Lower your deer range to 500yds and a 16" barrel gives you more milder options. You can still shoot steel and varmints to 1000 yds with a 16" in 6mmARC, 6XC, 6CM, etc. and deer to 500 yds. I don't think you'll like the muzzle blast of a 6.5/7/300 PRC or 300WM size rifles with a 16" and brake. You won't need a brake with those milder cartridges reducing muzzle blast.
 
I just watched a video of a Weatherby that has an 18" barrel with a 338 rpm hitting at 1000 yards with a light country weighs about 5 lbs.
 
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