I think I've finally managed to get quantum stockpiles to work fairly regularly, but there were a lot of initial troubles. I have a theory that wheelbarrows actually might block hauling of item to their own tiles (no proof), so my wheelbarrow equipped feeder stockpiles are now six tiles. It very easy to forget the dump direction of the Stop, as well, and no way to tell afterwards, but that shouldn't affect hauling to the feeders. I assume you have "no bins" set on the feeder stockpiles?
Also, I tend not to set up the feeder stockpile (or have it disabled with "take from links only") until I have a mine cart in place, but my latest stockpile worked without that restriction, so it might just be superstition. I DO create the target quantum stockpile at the same time as I designate the building of the Stop, as that means I don't have to remember which direction the Stop was supposed to chuck stuff in when it's finally built and the mine cart is in place.
Another thought: 7 dwarves, some of which are probably doing stuff full time (like mining), and multiple three wheelbarrow stockpiles MIGHT result in a job saturation issue (I definitely have no proof). You could experiment by reducing the number of wheelbarrows for each stockpile to 1 (meaning at most one hauling job was allocated for that stockpile), to see if things start to arrive at the other stockpiles.
The way I started my fortress was to define a stockpile for everything except wood, stone and refuse in the entrance corridor as soon as it was built, and then further stockpiles further in. The purpose of that was to get as much stuff as possible indoors quickly to reduce the risk of theft by local wildlife (previous experiences). Also, I created a moving meeting area on top of it to get non grazing animals indoors as well. It gets messy and cluttered, and you may get stuff in the way of your starting farm plot that way, though. However, initially a number of dwarves don't have anything useful to do since the space for their workshops hasn't been dug out yet (if I manage to get the stuff inside quickly, I might have them gather plants for a while).
I haven't seen rampant rotting from food in pots that's ended up in the furniture stockpile...
Hm, wait a minute: 7 dwarves, 3 wheelbarrow rock stockpile, two miners, one woodcutter, one farmer. Only 3 haulers left, and they all have all hauling labors enabled, I guess. I'd try to deassign rock and wood hauling from one of the "free" dwarves to see if it gets moving, as all 3 of them might allocate themselves to rock hauling, possibly without any rocks to haul, and too stupid/lazy to look further for work.