Obviously the least expensive means would be to borrow or rent or even buy a suitable trailer, and then use a launching ramp
somewhere convenient to you.
If the time pressure is not too great, you might print out some ads looking for a rental/borrowable trailer. Yacht clubs and many other places support bulletin boards for posting
such ads. You could try Sydney
Afloat or even here on CF.
1350 dollars to slip a 22 foot boat is outta sight. A less handy option is to sail to Tassie... lots of small clubs there with very inexpensive slipways... likely about 50 bucks for your boat. Last year we were on the hard
for two full days and our yard bill was 170 dollars, and that's for a 46 footer!
Another thought is that for the 1350 you could likely buy a decent trailer which would work for many years (if you had a place to store it).
Don't give up... there must be a better thing than the extortionate rates of the Sydney slipways!