Exact same symptoms for me - AC compressor cuts out when idling (no cooling), starts again when moving. I too had already replaced the 384 relay, so was pretty sure that wasn't it either.
Easy diagnosis as posted elsewhere:
With the ignition and the A/C on, the AC condenser fan should run (the fan on the passenger side), even without the engine running.
If the fan does not spin, remove the Power Steering reservoir cover (molded clips - pops off). You'll find 3 wire connectors clipped on a vertical holder. The AC condenser fan connector is the one with two large wires, a brown and a red/black. The brown is chassis ground, the red with black is power to the fan. Provide power to the fan side with a 12v source to see if it operates. I hooked a battery charger up to the fan connector and it did nothing.
AC condenser fan was dead.
I bought a very inexpensive replacement fan ($40) off of eBay and it fit and worked fine. Replacement procedure is:
1. Remove engine cover, plastic air filter cover & air intake tube that goes to the grill
2. Remove top portion of timing belt cover (2 clips)
3. Remove one phillips head screw on fan's top mounting point
4. Rotate entire fan assembly 1/2" in the unscrewing direction (counter clockwise) to release it from the fan shroud.
5. Remove Power Steering reservoir cover and disconnect the fan wiring connector (the one with two large wires, a brown and a red/black)
6. Jack up car and remove belly pan.
7. Use long screwdrivers (or similar) to reach several cable clips along the edge of the radiator shroud - open the clip with one tool and pull the wire out with another. Not easy to get to these, so it takes some patience.
8. Remove the old fan assembly & wire through the top (It is very tight, but can be done by carefully rotating and shifting the fan. I cut the connector off the old wire to make removal easier.)
9. Install new fan assembly - opposite of removal.
10. Reroute wire in same location as old wire and push it under the wire clips.
11. Reinstall belly pan, TB cover, air intake tube, plastic air filter cover, engine cover, wire connector and PS cover.
Less than an hour job, start to finish.