I concur with attibones, except that I suspect your silent cycle should work here. Two platies will not produce much ammonia, and with fast growing plants like Cabomba, Wisteria and Moneywort (all being stem plants, and stem plants are fast growing plants) this alone would not be an issue. So we are left with the acclimatization and/or the condition of the fish.
On the ammonia in the bag water, this is not to be wondered at. On the way home, those fish in the bag were under severe stress, and thus respirating more than normal and thus producing ammonia. This is one reason we want to get home fast and get the fish acclimated.
A brief explanation of how to acclimate fish. Float the bag in the tank as you did. I usually carefully remove some of the bag water first, as I want to add water from the tank. Wait a few minutes especially if to your hand the temperature between tank and bag water is different. Then add some tank water to the bag, making sure it remains floating and the bag water does not enter the tank through all of this procedure. Wait 10-20 minutes, then add more tank water. I usually add about half a cup to a cup each time, depending upon bag size. Do this a couple times. Then carefully net the fish out of the bag into the tank; do not pour them out, as bag water will get into the tank and this you do not want. Some fish take to a new environment readily, some do not. The stress from store to your tank impacts on this too.
Don't worry about feeding them for the first day or two. Leave them alone, let them settle. If they want to hide, let them. Once they are settled, and provided no injury was done, they should be OK.
On the temp, I agree this has to be resolved. Heaters often--very often--do not function at the set temperature. I have very good heaters that when set at 72F maintain the tank at 77F. This doesn't matter, but you do need a good thermometer as attibones said to know the tank temperature. The mercury glass thermometers are more reliable than the stick-on, and they come with a suction cup to attach them to one corner of the tank. Choose a corner away from the heater. Adjust the heater in stages as attibones said until the tank temp is around 76-77F. This is sufficient for platies. At higher temperatures, even though they can manage, they will have to work harder to carry out their physiological processes, and this wears them out. And you do not want to be fluctuating the temp like this, that also adds stress.
Keep us posted.
Byron.
