Suzuki ATV Master!
Join Date: May 2014
Location: Middle of Alaska
If I'm thinking right, your '87 has a round slide style carb.
With it at idle, adjust the air screw out until it starts sputtering, then take it in until it stops sputtering. Then go see if it does the same.
Did you verify that the pilot jet was the correct size?
Other than that, it seems like it simply isn't getting enough fuel. Maybe weak/dirty fuel pump? I know they make rebuild kits for them. Something you can try is to bi-pass the fuel pump. Just put a small tube between the ends. Then with the gas tank over half full, try it out. gravity feed should be fast enough to keep up, but will only work for half tank or more.
2013 Suzuki King Quad 500 AXi w/EPS
1990 Suzuki LT-4WD 250
and lots of snowmachines