The knot usually used to put a loop into the middle of a line is the Alpine Butterfly. It does not move like your prusik method, but it is easy to retie if you need to adjust the spacing.
The rest of your method is the way we might do it: main line over the branches and tied at both ends, carabiner or pulley on each loop with a "hoist line" on each, each hoist line gets a payload that is pulled up and tied off separately.
There are two other methods that we use depending on conditions. The first is the PCT method. Lots of descriptions and videos available for this just do a search. Nice because it only takes one branch and doesnt need a tie-off.
I dont know of a name for the second method, I learned it on bwca.com.
1) Rope 1: 25-ish feet with fixed loop and carabiner on one end.
2) Feed a longer hoist rope through the carabiner. Tie the hoist rope to itself so that it doesnt slip out.
3) Get Rope 1 over an appropriate branch as with other methods and tie off so that the carabiner is at least 4 feet below the branch.
4) Attach payload to hoist rope and pull away from the tree. Initially pulling will raise the load up to the carabiner, then it will pull the carabiner away from the tree bringing the food out into empty space. Tie the hoist rope just like you normally would.
You are creating a triangle with the branch as the top corner and the combination Rope 1 / Hoist Rope as the hypotenuse. You may need more than one of these setups, but you can put a lot more weight on this than the "main cable" method because the sag is not as much.
As others have said 14 is a large group. Leave No Trace considerations aside, you would be better off splitting the group, or at least using two hang locations. If you use a rule of thumb 2 pounds per person per day you are looking at 140 pounds of food for the group. To hang all 140 pounds (even decreasing by 28 pounds per day) you will need stronger ropes and higher branches to hang it all at one location.