Is AGM an option for this application?
ref 30secs to unscrew neg terminal; see the 'batt is in wheel well", behind fender part - not reasonable in this case
ref solar chargers; see the 'kept in garage' part. Have 120v however.
I can't think of a reason why an AGM battery wouldn't be an option. Whether it's necessary is debatable (they're usually recommended for cars with a lot of on-board tech, high-powered sound systems, and so forth); but they usually represent the top of a manufacturer's line, have the best warranties, and are available in most (if not all) configurations. I can't think of a good reason, other than initial cost,
not to use one on a car you plan to keep.
As for the solar battery maintainers, they come in two basic styles. One is designed to be hooked up to the battery and the panel secured on the roof or hood of the car, usually with suction cups. The ones I'm referring to for your mission have longer leads so the panel can be mounted on the roof or exterior of the garage in a sunny place. They also tend to have the controllers in-line rather than built-in to the panel because the panels also have other applications aside from trickle charging.
Most people have no idea how much power transformers consume even when they're not doing anything useful. Even
most phone, tablet, electric razor, and other portable device chargers suck enough current as long as they're plugged in to collectively make a noticeable difference in the average electrical bill. The draw on the primary side of a "wall wart" charger under no load is almost as high as it is under full load. (A few are smart enough to only draw full current when there's a demand for it and only a slight trickle when they're standing by, but they're the exception.)
Long story short, if your typical AC-powered battery charger is
capable of putting out 60 watts on the output side (as is the case with a five-amp maximum-capacity charger), then it's always consuming more than that on the input side (because transformers are not 100 percent efficient), even if you have it set to a lower setting for trickle charging, and in fact even if it's doing nothing at all.
Well-made, solar-powered battery maintainers with panels that can be mounted on the outside of a garage list in the $100.00 - $200.00 neighborhood, and can be had for less than $50.00 if you shop around. It doesn't take long to pay them off, especially if your electric rates are high.
One thing you should NOT do is splice extra wire into the leads between the panel and the controller. The resistance of the wire is factored into the system design. Adding more resistance will definitely reduce power output and might damage the controller.
Rich