As previously posted I would stick with the degree if you can, Im sure it will eventually pay off. Have you thought about GA or is it purely the big stuff you are wanting to work on?
If the Airlines have already said that you would be over qualified for an apprenticeship then does this not already answer your question?
As far as the exams go I would maybe check first on the validity of them without having the experience requirements?! If its all good then crack on, the exams are only available 1 day a month I believe so I am sure you would be able to work something out and you would maybe stand bigger chance of passing whilst you are still learning with the degree.
Just remember 17 months is nothing compared with the other 45-50 years you have ahead of you in your working life!