For Trap - in an over under I prefer a 32" barrel / and your 870 with a 30" barrel is about the same overall length ( butt to end of barrel ) as the over under with a 32" barrel.
For 16 yard Trap - using 1 oz of 8's - I like a Mod choke. There isn't anything wrong with a full choke but you're shrinking your pattern down quite a bit. You should try to shoot a trap target as it is still rising - so from the 16 yard line - that means the target is about 30 - 35 yards from you as you break it. Most 12ga guns will pattern a 30" pattern at 35 yards with a Modified choke - and the idea about chokes is to put a 30" pattern on the target at the kill range. To go tighter doesn't make you any better - it defeats the purpose of having a gun with a changeable choke in it.
You didn't really say if it has a changeable choke in your barrel or not - but if it isn't changeable just leave it the way it is. To really know what that gun and that barrel is doing at 35 yards - with any given shell - you should take it to a pattern board. All chokes and all barrels are a little different / and changing the load / changing a load with 8's vs 7 1/2's can open up or close up a pattern a little. So what I've told you is general info.
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