Did you see if you can take a train from LBJ to Salzberg and then to Innsbruck?
Use Austrian RW timetable
We only last week travelled from Ljubljana to Zell am see by train. We had to change Schwarzach-St Viet. This was quite simple. The train to Zellam see is actually the Innsbruck train. So there is no real need to go all the way to Salzburg and back out. We booked it the day prior from the station at Ljubljana. Our trip from Ljubljana to Zell am see was around 4-5 hours with the change. The price was around €95 for both.
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