Need HELP! on Bamboo quarter round molding

[DP Cowboy]

I recently installed bamboo flooring in most of our downstairs area. Everything came up roses...I am really happy with it...except...
The quarter round molding (which really does 'set off' the flooring against the textured drywall) also has to wrap around a raised stone hearth which divides the living room and dining room (one of those "two-way" fireplaces). Because the molding is not affixed to the floor, but nailed (so far) to the walls, I am just not sure how to attach it to the stone hearth w/ short wall (about 18" high) of the fireplace...and is there a good way to fill in gaps between the molding and the stone? Do I glue it with weatherstripping or something like that to the stone?
Thanks anyone for your help!