but the lady who answered my email wasn't able to answer specific questions about the whole process and referred me to Austrocontrol. She was saying I would have to first get the PPL, then CPL(A), then IR(A) before I could even start with the distance learning for the ATPL(A).
Same experience exactly as I had. I was told to contact Autrocontrol for the specifics, and they referred me to asking at the flight schools.
It is
not true that you have to get a PPL, etc... to start with the DL!
Seems she really got no clue.
You may want to try to contact Mr. Hans Eggl, he is the head of training (or something like that

) at FlightTrack, a FTO in Salzburg. They were the only ones helping me out a bit, even though their prices are rather on the steep side. You could at least ask for the specifics, they are quite helpful in terms of what you have to do, really. Make sure you give him your license details and TT when first e-mailing him, will make it faster.
Good luck!
INNflt
edit: BTW, as for getting into Tyrolean Airways, don't keep your hopes too high - their future is very uncertain with all the troubles Austrian Airlines (they own them) is in. Most important part will be whether Lufthansa decides to buy the Austrian Group or not. Recruitment won't probably start for a few years.