Similar Experience - Hesistation
I had a very similar symptom recently with my Phase 1 V6 GTV. Hesitated when cold, slightly lumpy idle and my fuel injection light was on. Took it to the garage..... no quick fix available so I took it back.
The problem ended up being a faulty relay under the RHS cover panel in the engine bay. The relay was triggered by the fuel pump relay and is responcible for supplying power to the air flow sensor. When I tested the plug at the AFM, I didn't have any power. One of the pins should have 12v with the ignition on.
Anyway... replaced the relay, now had power at the AFM. Reassembled air intake, started engine and presto... smooth idle, hesitation when cold gone, check fuel injection light gone (it cleared itself within seconds of starting the engine).