Not all AGMs are deep cycle. FWIW, I think that you need to do a bit more research from a site that is not trying to sell you their battery. In other words, get some unbiased input. There are sites such as
www.batteryfaq.org that are good but perhaps somewhat dated. I like
www.windsun.com. They are a solar power website and store, and they have great technical tutorials to educate potential customers. They do indeed want to sell you batteries (and solar panels and controllers and chargers and cables ...), but they carry all types of batteries, and they want to sell you the right type - and that means educating you so you can choose the right type. Their long-term goal is to make sure they sell you a battery that meets your specific needs, so you will be happy and come back to them.
As for winter storage, any lead-acid battery, whether flooded, AGM, gel, or whatever, loves cold. The colder it is, the less self-discharge there is, and self-discharge is what you care about. I've told this story before, but I'll tell it again. I have a 1998 Ford Ranger that lives at my home in Maine. When we leave for Arizona in November, I put the Ranger in the garage and disconnect the battery. It sits there all winter, undisturbed, in temps from zero to 20 below. When we come back in May, I reconnect the battery, and it has never failed to start the engine on the first crank. By the way, this is the OEM battery, now 10 years old! So the important thing about winter storage is charge it, disconnect it, and leave it alone. No matter what kind of battery you have, this is the right procedure.
By contrast, I leave a car in Arizona in the summer, and I treat it the same way. But summer temps in Arizona routinely run 100-115 degrees. And batteries out here routinely last two years. Heat kills, cold preserves.
As far as the "box of toddler death". I hope you don't base a purchase decision on such hyperbole. In order to get in trouble, a toddler would have to set up the TM, unlock the battery compartment (batteries are locked in an outside compartment in a 2720SL), disconnect the battery cables, reach in at a highly awkward angle, lift a 60-pound battery straight up, and carry it outside. I have trouble doing it myself, and I'm no toddler. Just my thought ...
Bill