Sounds like you may need a new distributor. I had a car do very similar stuff. There is no way to test one except to have a friend loan you a known good one. I've had to replace the distributor on 2 of my past cars. Of course I am assuming you only replaced the cap and rotor since you have that in parentheses.
You can't lose if you put God first!
1989 LX, 306 with TF top end kit, Anderson N-21 cam, TKO 600 trans with steel splatter shield,full Maximum Motorsports Mustang maximum Grip box, Detroit locker rear end with 31 spline Moser axles. Staggered wheels with Nitto 555 315/35/17 out back.