Welcome to the board and boy, isn't your first post a doozy!
First off, congrats on your tank. Secondly, I think rather than buying any "live sand and washing it" (I'm not really sure what that means, by the way, the term and the action contradict each other)I would buy some bags of "dead" dry sand, put it in the empty tank or tanks and then use sand from the existing tank to seed the sand bed. You'll have to make up the substrate depth in the 75, but you could do that slowly, so as not to smother the critters living in there.
If you can at all leave all the corals in the tank, even if they are crowded, I would do so for now. Setting up new tanks, even with "borrowed rocks and sand" is going to mean a mini-cycle for the tank. With the move and probable mini cycle going on in the 75 as well as putting the corals under minimal lighting they are going to be stressed big time. If you just can't get them all in there I guess your only other option *is* to set up one of the other tanks. Be prepared to monitor water parameters and do several water changes, especially as you will have no skimmer. I'd make sure you put an extra powerhead in there for water movement, too. As far as what will do best under minimal lighting mushrooms, zoanthids, polyps, some leathers (not the yellow ones!) and anything non-photo (some gorgonians, etc) may do all right. It's hard to say without knowing exactly what they are and what light they were accustomed to as to how well they will fare. That's going to take some monitoring on your part. Is there someone experienced close to you that can give you a hand right now? How about the person who sold you the tank? Experienced observation would be a big help to you right now.
I'll recommend "The Natural Reef Aquarium" by
John Tullock, "The Practical Guide to Corals" and "Aquarium Corals: Their Care and Husbandry" both by Eric Borenman and "Corals: A Quick Ref. Guide" by
Julian Sprung right now to help you get aquainted with the hobby and with coral appearance, care and placement within the tank. Feel free to ask away here, we'll try to help as much as we can.
Hope this helps,
~Alice
Oh, one very important question: What were the smaller tanks used for previously? Cerain meds used in fish disease care are deadly to corals and inverts and the tanks may need special cleaning before they can be used.