Minecraft Tree Tipper Command Block Error

I am trying to create a system that when you break any block on a tree, the whole thing will break. I successfully made that part, but ran into an error. I have it so the tree is relative to a bat named Tree1, so anywhere there's a bat named Tree1, there will be a tree. What I am having a problem with is that when ever I break a block on one tree, it affects all of the other trees. I need to know how to have the same bat under each tree(no differences what so ever), then somehow change the bat once it's tree gets chopped down. I could set it so that the player receives a scoreboard point when their holding an axe, and the tree would only fall when that player is in a certain range, but that might get messy around tress that are clumped together, and I also want to keep it as compact as possible. Here is the code:

Spawning the bat:

/summon Bat X Y Z {NoAI:1,Silent:1,CustomName:"Tree1"}

Setting the scoreboard:

/scoreboard objectives add Tree1 dummy Tree1

/scoreboard players set @e[type=Bat] Tree1 1 {CustomName:"Tree1"} (on a setblock clock)

Spawning the tree:

/execute @e[type=Bat,score_Tree1_min=1] ~ ~ ~ /fill ~ ~2 ~ ~ ~7 ~ log /execute @e[type=Bat,score_Tree1_min=1] ~ ~ ~ /fill ~-1 ~4 ~-1 ~1 ~8 ~1 leaves 1 replace air

Testing to see if a block is broken:

/execute @e[type=Bat,score_Tree1_min=1] ~ ~ ~ /testforblock ~ ~3 ~ air (on a setblock clock)

Using a comparator to remove the tree:

/execute @e[type=Bat,score_Tree1_min=1] ~ ~ ~ /fill ~-1 ~2 ~-1 ~1 ~8 ~1 air

Spawning the dropped items:

/execute @e[type=Bat,score_Tree1_min=1] ~ ~ ~ /summon Item ~ ~2 ~ {Item:{Count:4,id:log,tag:{display:{Name:Wooden Log}}}}

Any help would be useful. Thanks.