They do not make an Eco insulated 1.28gpf model.
They do make the G-max ST743SD 1.6gpf.
They have generic insulation kits available in the big box stores you can modify to work you just have to check to make sure it doesn't get in the way.
Ahhh the kids are still test flushing the toilet huh...
You must be going through a bunch of toilet paper.
Another option to cure the sweating tank is installing an Anti Sweat Valve in the feed to the toilet. The valve mixes a small quantity of hot water with the cold supplied and brings it up to ambient temperature to eliminate the sweating. This device is quite common on older homes in the northeast but virtually unheard of in some other areas of the country...
Price guestimate about $30.
They come fixed and adjustable...
I don't imagine being a distance away is bad as long as the water in the pipes will not cool back off below the temperature inside the house...