Get a large plastic container / new plastic garbage can and move the water from the tank into this container keep a heater and something to provide oxygen to the fish. Put your corals in another seperate container with water from the 75 gallon. Try to keep all of the water from the 75 that you can. Then move the current tank, put the new tank in it's place, add gravel rocks, new water plus old water, corals, then add fish and water from the large bin / container.
You may have a little die off from rocks /copepods etc, and if you are moving the gravel, will probably be a little cloudy, but with a little help from one or two friends you should be able to get this done in 4-6 hrs. I have done it twice and never lost a fish or a coral.
Tank should not recycle, die off should not be significant, and you will be moving all of the good bacteria with hopefully limited die-off.