A lot of good advice here. As for the coral I could not access the link, so I cannot weigh in on what you paid. Don't think dead coral is a bad thing. Many people including myself use for decoration in FO
or FOWL systems. Live coral is nice, but very costly and only for an established SW
system and well read experienced aquarist.
More importantly I am concerned about the fish. In a FW
system you may be able to get away with transferring fish like this. Hopefully you can find a good temporary home for them.
If you cannot find a home for them and have no other options I will say that BIO-Spira is an option and I have used it myself to help rapidly cycle my 75 gal
. It is very costly and I would suggest getting two packets for this kind of load(I think it only comes in one size for 55gal). I would also put all the filtration you can fit onto the 75gal for now.
One thing you did not state was how far you had to travel to pick up the new system. The beneficial bacteria in the existing filters on the 55gal will only survive about 2 hours(possible longer) with no significant die off once you shut them down. If you can get them on your 75 right away it will help some as well as some of the water.
If you use the BIO-Spira follow the directions and do not add it until about 45 minutes prior to adding the fish.
I think the overall best option would be to see if you can postpone pick up of the 55gal until your system has properly cycled(3-4weeks) if the seller will allow you to do this. The fish will ultimately be to big for your system, but if they are doing well now you may be able to keep them for a while and them move them out over time as they grow.
, welcome to the hobby. remember Reading and patience are the key to success in this hobby. This site is a great place to learn. You can never do to much research.