1987 Honda CRX 1987 Honda CRX Si, timing WAY off

I recently acquired a CRX Si whose timing belt had snapped, after only 30,000 miles according to the service records: The previous owner had all major work done at the dealership, and kept all records.

I installed a new timing belt, water pump, plugs/wires/cap/rotor, air filter, oil change, timing cover gasket. I adjusted the valve lash. I did not service the valves or pistons: I wanted to see if it was still OK. I siphoned the gas tank and added new fuel (it's at least half new fuel, half old).

The old spark plugs were badly fouled with heavy carbon deposits.

The engine turns over, sparks on all cylinders, but does not run on its own. If I depress the gas pedal a bit, I can get the engine to start and run. It will run as long as I keep my foot on the gas, and holds at a steady RPM. I can operate it through the full RPM range above 1000 RPM, but it runs a bit better at higher RPM.

I checked the timing (roughly), and it too far advanced. I cannot retard it any further because the distributor is at the end of its adjustment range, and the distributor connects directly to the end of the cam shaft (no gears, I can't just move it one tooth over).

Is the problem in the distributor, ECU, vacuum system, a bad sensor? I'm wondering where the trouble is.