Sell your existing lift and buy new at your destination city.
I moved from Northern Illinois to California in December 2010. I had a 2 post lift in my garage, along with a metal lathe, vertical mill, sheet metal brake/shear/slip roll, 80 gallon air compressor, band saw, welders and other tools. I did the move myself using ABF's "U-Pack" service. I built crates for the tools and rented a fork truck to load them into the ABF semi trailers, bought a used pallet jack to move them around in the garage and in the trailers and rented a skid steer loader with forks to unload them (driveway was too steep for a fork lift). Lots of work... Even with all that, I had no desire to try to move the lift since it's just so big and a hard shape to pack around.
I sold the old lift on craigslist and bought a new one in California. I had other people say, "You should just sell everything and buy new" but that would've cost a fortune since most used machine tools go for a fraction of new. The lift, strangely enough, sold for $50 less than I paid for it.