VVT-i actuator is unlocked? Not sure if you sent the whole head in, or took the cams off. The timing gear should not be locked when you reassemble the engine. This could cause the install to become much harder to do + the timing is offset. Same goes with the camshaft position sensor - these can get damaged, causing intermittent output - confuse the PCM.
I'd double check all the simple stuff - vacuum leaks, bad/damaged sensors, pinched wires, corroded connectors (corroded surprising quickly when the engine is apart for rebuilding - depending on where the parts are stored), etc.
Getting good spark on all igniters? Could be bad connections, damaged PCM, pinched wires, etc.
Getting fuel to all plugs - possible bad injector, injector leak, damaged fuel rail, leak at fuel line, fuel pump bad, bad electrical connections. Pull plugs after it cranks and dies a few times - the plugs should be wet or smell heavy of fuel.
These heads are quite unique - they cannot be rebuild in the same was a traditional head. Example: The water jacket is so thin in places, like the valve seats, that they do NOT recommend cutting those seats. That material is powdered metal that is laser clad to the aluminum casting. There is a little bit of meat there, but shouldn't really be cut, as the water jacket was design to expose that area directly to the coolant, faster heat dissipation. Head shouldn't be decked either - if it is warped beyond a certain tolerance, the factory service manual says to scrap it. Don't try and cheat and use a thicker head gasket - that will automatically fail in short time.
Did the shop give you a print out of the measured clearances? There is actually a typo in one of the repair manuals for the valve specs - I can't remember which publication it was, but it was off by something like 10/thousandths?? Could be an issue, depending on how they rebuilt it - some shops like to push the starting clearances looser than spec, so as the parts break-in, they will close up that clearance.