Engine cuts in and out at low level throttle position.

All sensors? That's a ton of money! Usually, the cause of hesitation on acceleration is a spark plug wire. A worn out TPS can also cause it. But you said that you replaced all the sensors and plug wires. Distributor and Throttle body have nothing to do with your concern. It won't run with a distributor concern. The Throttle body really only affects Idle. You can remove the throttle body and clean out the IAC and the Throttle plates. A sticking IAC might contribute to your concern. Have you checked the EEC-IV system for codes? It doesn't have a MIL (Check Engine light), so you wouldn't know if there are any codes unless you check. The only other contributor besides a failing Ignition Coil that comes to mind is the MAP sensor - but you said that you changed all the sensors.