Ah, that's a tricky one.
I had the same problem on a recent tank upgrade. What I did was water change about 25% out of the tank I was using, and put that water into the new tank. Then I topped it up to about 50% full with fresh mixed salt water, and got the heater working. Then small water changes for a few days to top it up further to about 75%, and occasionally moving some live rock pieces in. Then on the changeover day I topped it right up with the old tank water and moved the rock over aswell. This left the fish & critters etc. in a small amount of water in the old tank, easy to catch and move over into the new tank.
Admittedly mine was only about half the size of your new one but it worked ok for me. No fish lost and all doing very well now thankyou.