The only sure way to avoid excess baggage charges is, I regret, not to take any excess baggage! You could explore airfreight charges, but I think that will be expensive, plus "handling & documentation charges" at each end!
I would suggest road transport as being the most economical and simple method, you could Google something like "freight forwarders Austria" - I'm sure there'll be various companies who could give you a quote. They'll want to know the aprx total weight and volume. Also, ask for their "door to door" and "depot to depot" rates, for your cost comparison. I'd guess a 4 to 5 day transit time would be expected.
Good luck!