To get the plunger out I would completely strip the carb and use a bit of heat on the body of the carb where the plunger is some penetrating oil to loosen the plunger up. Then use a pair of needle nose pliers and a small tip straight screwdriver to twist and pull plunger out. It takes a bit of time especially if the piece is really stuck in there. Ive done 2 dx carbs like that. Just dont scratch the walls when you are trying to get the plunger out. All of the parts you for the plunger you can buy and for a carburetor rebuild kit just use one for a yamaha 250 timberwolf, just use your old jets because the timberwolf ones are different . And if you need a choke cable use the one from the timberwolf as I believe the dx cable is discontinued.

This is a timberwolf carb I rebuilt for my dx. They are basically the same other than the jet sizes
1979 ATC110
1983 ATC110
1984 ATC110
1984 ATC125M
1985 ATC110 2 of them
1985 ATC110 The wife's
1987 ATC125M
1985 ATC250ES
1984 DX225 with 250 timberwolf engine and swingarm. Wolf in DX clothing