Hello, my name is Mark and I will try help you with this.
The vibration you felt was probably a misfire from the engine caused by the faulty injector. If you intend to drive it 400 miles with this fault you will probably cause serious damage to the engine and the exhaust dpf system.
I'm surprised though that this isn't covered by either warranty or at least a goodwill contribution from VW due to the low mileage and age of the vehicle. Maybe you didn't ask.
The price quoted is actually quite good to replace an injector as they are very expensive to buy. They can also be difficult to remove due to carbon build up on them.