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.