I have a similar background - I started learning to fly when I was an aeronautical engineering undergraduate - got my PPL just after graduating, and then decided that I loved both flying and engineering and was going to pursue both.
And I have - it's 19 years since I graduated with my first degree, and in engineering I've gained CEng and a PhD, whilst in flying CPL & CRI (and needless to say, quite a lot of other things in both fields, including clocking up 97 types in my logbook, 63 of them as PiC).
With a fresh masters you are just about employable in engineering, and with a PPL you're a little behind that in flying but in a position to gain professional qualifications. Under EASA you'll even be able to teach on a PPL and get paid come a rule change next year.
So, I think that you have three choices, and they really come down to your personal aptitudes and passions:
(1) Ditch the engineering, become a full time professional pilot following the usual career route.
(2) Accept just being a keen PPL, maybe doing a bit of weekend instruction, and concentrate on building your career as a professional engineer.
(3) Build parallel engineering and flying careers - which will potentially open up the sort of stuff I've done for the last 20 years - flight test engineering, test piloting, and research flying.
Lots of people can talk about (1) and (2) - (1) in particular is covered by numerous threads on Pprune. On the other hand (2) you'll find plenty about in literature from various engineering institutions and large employers.
(3), which I can talk about with some authority, will make you an oddball - you'll be unsuitable for a lot of mainstream jobs in both engineering and flying. You're unlikely to be expert enough in any particular stress or CFD package to get a top-paid job in a design office, whilst you're unlikely to have the large numbers of hours in particular types / kinds of flying to get a well paid captaincy.
However, speaking for myself - I don't care. Operating a CAD system 40 hours a week, or driving a 300 seat bus 800 hours per year, would strike me personally as narrow and dull.
So, I've back-seated fighters, observed trials on board an aircraft carrier, presented papers all over the world on various aspects of aeronautics, designed bits of various aeroplanes and helicopters (and briefly, a satellite, although it never got launched), crewed 10 first flights of new-build aeroplanes, 6 of them as PiC, given evidence to my country's parliament, never been unemployed, not struggled for money since I was about 30, and continue to have a huge amount of fun. And I still would be unemployable in a stress office or an airline cockpit.
Truth is, I'm a good but not exceptional pilot, a good but not exceptional engineer, and have also discovered that I'm a good but not exceptional manager - but I'm lucky enough to be able to be good at al three at the same time, which has been my edge so far.
So, I'd say work out which of engineering and flying are where your real skills and enthusiasm lie - and then work out which way to go. If you have enthusiasm and a high degree of skill in both you might want to consider following me, if you have skill as an engineer but only really enthusiasm as a pilot - become a professional engineer and keen PPL; if you have real skill and enthusiasm as a pilot and only really tolerate engineering - ditch the engineering and become a full time professional pilot.
Which is a problem only you can solve - the rest of us can just present the options for you really.
I'll offer one other opinion however - at 22 you really don't need to be in a screaming hurry. Use the next 4 years or so to get yourself on the right path, without killing yourself or destroying all joy in life. There are plenty of people who have established themselves as professional pilots or professional engineers in their 40s - you are well ahead of the game.
Actually one last opinion, don't work anywhere that might jeapordise your flying medical. A paintshop with no respirators available is definitely one of those.
Okay, yet another opinion having re-read your original post. All three of the options I've laid out start with a PPL. I'd recommend getting your PPL reasonably soon, and discovering how well you can fly, and how much you really enjoy flying. Stop mucking about with ATPL exams until you've got that and done at-least a bit of flying as a licenced PiC. Until you do that, you really don't know how good you are as a pilot, nor how much you really enjoy it. Saving up to do your PPL in the USA with one of the JAA schools in Florida *may* be the way ahead there, although do recognise that the USA is not Europe so you'll have to do some instruction when you get back to learn how to fly at home.
G