A modified is plenty of choke at 16 yds.../ if you are not already doing it, you need to be shooting a Trap singles target as it is rising, not as it flattens out or starts to fall. ( kill range is at 30 - 35 yds from the point you're standing...)
As far as shells go ....1 oz of 9's or 8's are plenty of shot, with a Modifed choke as well...at 16 yds ...in fact, it works just fine to about the 20 yard line ( because you're still killing the bird at under 40 yds total distance)...
( if you're shooting bio-degradeable targets...they're a little tougher to break, so I'd stay with 8's over 9's ).
...as you move back from the 16 yd line. 21 - 25 yd lines I would go with an Improved Mod....( because your kill range grows to 40 or maybe 44 yds...
....and if you are shooting at 26 or 27 yds, I'd go with a Full choke - and I'd move up to pellets at 7 1/2's ...but I still stay with no more than 1 oz of shot.
Some of my buddies use the same chokes....but for Trap, all they shoot is 7/8 oz of shot...same as I do mostly with 8's...
But the real key in shooting Trap singles, is to kill them when they are still rising and under power - so the flight is predictable.