Newspaper is not adequate for cold temperatures. I would use styrofoam, or typical insulation like you find in your home. Water is not as important as air. Have just enough water to comfortably cover the fish. Also, use thick bags for big fish, don't use a breather bag. Heat packs also absorb oxygen so they would remove all the oxygen from the water in a breather bag. A regular bag is fine though. Assuming your big cichlid is around 9-12 inches, I would ship it in a 18" x 18" box. If it's smaller a 12"x12"x6" box could work. Where are you shipping the fish? UPS ground overnight shipping could be cheaper. Also, you may have to go to more than one USPS to ship the fish. One USPS near me refuses to ship any liquid by air (priority or express). The rest will ship fish by air. Some people coat the whole box in tape, I do not. I leave little areas open for oxygen to get into the box. Fish bags tend to slowly leak air/CO2, and your heat packs also need fresh O2.
You can get small amounts of bags and heatpacks from aquabid, or you can see if your LFS may sell some.