Arowan and Celine - The move was successful. :) Here was my strategy:
Tupperware bowls. Lots of them. One of them contained my fish since he's too big for his cup.
Another Tupperware bowl was full to the brim with water and my filter media.
Another Tupperware bowl was full to the brim with water and my plants.
Another Tupperware bowl was full to the brim with water and more plants.
My heater and filter were stored in a bag.
My tank was drained to where the water laid just above the gravel.
Once I had my plants and fish out of the tank, I stirred up the gravel, then siphoned out the dirty water. I dumped that water. The rest of the water, the stuff covering the gravel, remained in the tank so that acclimation was easier.
I hope this helps everyone. :) Message me if you have ANY questions.
I kept the cleaner water in the Tupperware bowls and also added it to the tank. I also let the filter cycle the tank water to clear the water before I started thinking about adding my fish back in. You know how plant matter and diatoms can make a mess of things...