Children and firearms mean a certain amount of compromise is necessary between ready access and safety. I think your current solution (magazine loaded, no round in chamber, stored in a high place) is a viable option.
However, if you would like to have faster access to it, while still keeping it safe there are many childproof safety lock devices similar to the
Lifejacket that let you store a longgun near or on a bed; but make it impossible for a child to use it. Most are under $40 as well. They will also slow your access to the firearm; but if you get to move it from the closet to someplace more convenient, that may not be a bad trade.
You might ask this question in Shotguns as there are a lot of people there who are familiar with the 870 and safe storage of it around children.