Melaine here are my recommendations:
Use your 10 gallon tank as a QT. Bare bottom, no substrate. use 10 gallons of water from your display to start this tank. Use a HOB filter with a sponge. Possible a power head in the tank to keep a good flow. You may want to set it up under your display, if you have room. It will also need a light.
Move what LR you have, in your display, to this tank as well as your livestock. Plan on leaving it there for several weeks
In your display, get rid of the plastic corals. Remove the subatrate and wash it well with clean saltwater or discard and just get more. Fine argonite is great. If you get new substrate, save a few cups of the old to seed the new. If you get new and seed, place some new then disperse the old and place more new on top. Like a substrate sandwich. Or just replace half of it with new. Cost may be a factor. So go from there.
Get all new LR. A minimun of 1 lb per gallon. Preferably, 1 1/2-2 lbs per gallon. Do not skimp here, this is your main filtration. If cost is a factor, I'd keep the old substrate before skimmping on the LR. You may want to check into
www.tampabaysaltwater.com. This LR is some of the best you can get and they are located in Tampa. Perhaps you can go there and pick it up. When you get your new rock, aquascape your heart out! Pile it up in an attractive way. Make caves and overhangs so that water can flow in and around the LR. Get a good power head. The Koralia line of PH's are great and affordable. Get that going in the display so that the surface water is moving.
Remove the bioballs, filter floss and discard. You do not need them with adequate LR. Just let the water fall into the sump. Later you can add some LR in the sump.
Second most important thing is a new skimmer. The ASM line is very good. Consider a G1X or a G2. Make sure you compare the foot dimension of the skimmer with what available room you have in the sump. Get the one that fits. You could consider getting a bigger sump that fits under your stand that already has a refugium build it. Again, this is more cost, but is a consideration.
Recap:
1. Set up QT
2. Move Lr and livestock
3. Clean old sand and reuse; all, half, or none.
4. Get new LR.
5. Get new skimmer
6. Consider new sump/refugium.
7. After setting this all up wait for the cycle to end then return your livestock