Hmmm. Any chance you can look at the assemblies in place under the hood and take pics? If the turn adjust system is pranged then it could make sense but I am about 12 years behind in headlight tech. There should be a couple mounting screws or bolts, then adjusting screws if fixed. The bumper may need loosening but probably not removal. Keep us updated.
You cannot see the headlight assemblies from inside the engine compartment. At the back edge of the fascia there is the radiator with panels to either side. I do not know if the panels are structural or just to force air to go through the radiator, but the effect is that the entire back of the fascia is closed off.
Removing the front fascia should not be an enormous ordeal, although there apparently are a lot of fasteners involved. Sometimes installing a PPF to the fascia is enhanced by removing the fascia so that the PPF can be wrapped around the edges. I think the bottom pan has to be removed first and I believe it alone has 19 fasteners.
$3000 for labor seems rather excessive for a job that should take a couple of hours at most. Perhaps the cost of the headlights was included? This labor cost is a concern relative to buying the MOPAR CF front grill, which requires removal of the fascia to install.
The European headlights have an "autolevel" feature. I do not know if the NA spec headlights use the same assemblies, but MacGeek pointed out that the rest of the autolevel feature is not present on NA Giulia (some websites state that bi-xenon headlights in the NA market are required to have autolevel). I do not know if a malfunctioning autolevel function could cause the O.P.s issue.
Autolevel has the potential to point the headlights straight into the ground when driving up a steep grade. I sure hope my car doesn't do anything like that.