Being Australian myself I do understand that you want to see everything. You have been given some great advice here about slowing things down. I would suggest removing Innsbruck it is a pretty town but incredibly boring. Switzerland is stunning but expensive ( think high end Sydney prices for anything basic). Your budget is fine as we usually allow 200 euros per day for eating and day to day stuff for our 89 days every two years. We rarely spend that and it does give you freedom to do what you like.
You could be a bit light on for accomodation but if you don't mind hostels ( they can be a bit tacky). Our daughter does 4 days hostels 3 days somewhere nicer.

Most importantly you are on holidays and that can get lost sometimes in the planning.
Happy planning and good luck.

I agree about double checking your travel times, for instance you will not do Kalambaka to Athens in 4 hrs unless you have a car! Also agree 2 nights there is better, we stayed 4 nights
If you do need to schedule in thessaloniki because of travel times it's certainly worth a stay there too, we are here at the moment for our 2nd 5 night stay. The city often gets overlooked, but has lots to offer.
I got exhausted reading the rest, so yes, do narrow it down to less places & see them, no t just pass through

Kalambaka - Athens is 5 hrs by train, dp 5.42am and 5.32pm

<< You are allowed to make entry without a visa (for a US citizen in this case, yes?)>>

No. They're Australian. Americans do not quote prices in Australian dollars.

To the OP: you need to check out the possibility of cheap intra-Europe airlines instead of 10+ hour train trips.

Neckend, that's what the timetable says, but in my experience it's always at least 5.5 hrs
I live in Athens & never caught a train yet that arrives at the time stated, even though they leave on time!

....not exactly, the timetable says 4 hrs 40 min, I already rounded up to 5hrs, but obviously not enough!

I too think you have way too many places in the amount of time you have. One night stands are NEVER a good idea since that usually means you have only a few hours for sights/activities and they are likely to be late afternoon/evening. Unless you are willing to do a lot of 6 or 7 am trains to get to places in time to actually do something there.

But I'm old enough to be your parents and this trip would kill me. (Although my first trip with by BF when I was 19 we did many fewer places, in a car that his brother was driving - and our using it for the trip allowed it to be imported as a used car for way less in taxes.)

BUT, a couple of years ago by 19 yo D went with 2 friends and in about 6 weeks they did 8 cities (with some day trips) and felt that they needed more time in many places. Also she spent $8,000 US - so about 10,500 OZ $ - and that did not include any shopping and very limited student budget nightlife. So for 4 months that wold have been about $24,000 Aus $. But you have MUCH more train travel than they did - so I would assume your costs would be significantly higher. And you would need to avoid any typical tourist night life which could be much more expensive.