I would suggest this (adapt as required)
1) get some microbacter7 - this will accelerate your cycling - get an ammonia badge/ammonia absorbing sponge
2) start seeding the rock you will use in your 125 by putting it in your other tanks now (where possible you may have some real big pieces. This will limit the time you have to aquascape everything so you'll have to think through where all the rock will go and how they will fit together first. You can even get some filter media (those tube things but I don't recom bioballs) put it in a media bag and put it in your current system to start seeding it with bacteria.
3) get your sandbed ready - wash it out (you can use tap water and then just add a few drops of prime) - then store it in a bucket with "old water" from you water changes in your current system.
4) start saving old water from your current system water changes where possible
5) once you have your tank in place - put in the sandbed with the old water - install your rockwork and use as much old water as you can to fill tank.
5) get your new plumbing going (sump,returns mainly)
6) add the microbacter7
7) if you can hold off moving your corals so much the better, if not, then move them. just keep in mind you may get a diatom spike with any new tank.
8) monitor ammonia levels 2x a day - be ready to do major water changes (if necessary).
Your coral list has all fairly hardy corals - so you're in good shape.
good luck!