I've got an AR-500 plate that measures 12"x12".  Put it out at 800 today and did OK with the .308.  What size target are you using for 600-1000 yards?  I'm thinking that size of a target is getting kind of small for anything much farther.

Past 750 I use mild steel.  I keep a 18x22 piece at 1000

I used a 12x16 to 1k with my 308. With 185 juggernauts I was at about 30% hits. So that was a bit too small. I was doing about 1moa at 600 so the 12x16 was a bit big.

Different range now that has different sized plates at several at several ranges. Most are too big for hit or miss so I just observe group size or go for speed out and back, at 500yd they go from 12" down to 3" so that is fun.

Shooting 230OTMs out of my 308 at 1050yds I am about 100% on a 24x24 in an easy wind.

I guess I  would recommend a 100%silhouette,  it will be too easy for close up like 600 so you can shoot for groups or head shots and at 1k you wont be sending very many into the dirt but still be challenging. Many sizes are more fun though.

That's too small for .308 Winchester.  Your bullet is coming down like a mortar round at 800yds.

For a 6.5mm, 12" plates at 800yds are fun.

Once you start getting out to 1000yds, reduced IPSC are good for capable rifles.

For .308, you'll do better with a large gong, as long as it isn't angled downwards, which will work against the .308s danger space.

I've got a 16" round plate that's fun at 800-1000. 12" plates for anything closer.

I have a reduced silhouette that is a challenging target.  It is easier if I set it up in a barren area or against a dirt berm so I can see misses.

Generally speaking, it is practical to run 2 minute targets.  Obviously, for further distances, you may want to go with 3-4 minute size targets.  

I run one minute targets out to 300, and use them for positional practice.

if you're just having fun, it doesn't really matter.  
if you're trying to be practical, then use targets slightly smaller than what you would actually be shooting at in whatever practical scenario you envision, so you understand your capabilities.    Note that in practical scenarios, targets don't get magically larger as they get farther away...  so it's really more about knowing how far away your limits are

but for matches, inside 1000 yards, the 1.5 MOA for prone targets and 2.5 MOA for positional is a good guideline, so go smaller if you are practicing, larger if you're having fun

Beyond that range, here's an example of the targets past 1200 yards in the ELR PRS match in Wyoming last year:

(how many attempted shots, distance in yards, size in inches and shape)
3x 1266 30" circle
3x 1749 40" circle
2x 1220 antelope
4x 1215 24" circle
3x 1396 50% elk
3x 1278 50% elk
3x 1420 24" circle
3x 1710 30" circle
3x 1224 wolf
4x 1529 elk
3x 1442 24" circle
2x 1200 24" shot strong side, 40" shot weak side
3x 1283 antelope
3x 1770 wolf
1x 1217 20" circle
1x 1516 30" circle

As you can see, most of those are a hair under 2 MOA.   Some of the animal shapes e.g. wolf, are more forgiving on wind and a lot less forgiving on elevation

there's no set standard to compare yourself to, but that should give you some idea of what others are shooting at.   also consider the NRA F class scoring rings.  5" at 1000 for the x, and 10" for the 10 ring.  but you get sighters and shoot the same target 15-20 times in a row.  it's a lot harder when you have UKD, changing directions and positions etc

Just curious what steel are most of the targets? Do people still use ar500 for targets at 1000 yards or what are most of them made of?

1MRAD subtend for the easy targets, 1.5MOA subtend for the "challenge" targets. That's exactly how big. The size in inches changes with distance.

BC zone IPSC, leaned back on 2x48" rebar.  

gives me approx. 20-degrees facing skyward.  cheap and very easy to setup

I have a 4" round AR500 gong at 500 meters for my 6.5x47 GAP Crusader.

We were using a 10" circle at 950yds the first time I shot that far.  It took 10.6MIL elevation and .1MIL  windage.  I got my first it on the 3rd round after moving out there from 500yds.

I was using my 20" AIAT in 308W and 168gr BTHP's and was hitting 50% or a little better.  I hit 4 in a row once which was awesome.  It was about 82F with 50% humidity and 1800ft elevation.

I was happy with my first ever outing at over 400yds.

I bought a Magnetospeed and will be checking my velocity tomorrow as I have never checked it before.

I plan on trying out 1400yds with the 178gr ELD-X when I can on a 12" square plate.

ETA: I may throw on the 24" barrel for the 1400yd endeavor.

You're a great shot being able to hit a 12" plate at 1400 yds with a 308. I would personally use 208 or a 220gr projectile at that range.

100 extra fps from the 24" will raise your hit probability from 7% to 8%.
Just going to a 200.20x will raise it from 7% to 9%