This solution is untested.
You Only Need Six
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| . . . . . | 0 . 0 0 0 . > ^ ^ ^ . | . . . . . |
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Label the Bouldrs:
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| . | G | - - - - - | ^ | . . . . . |
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| . . . . . | D . C B A . > ^ ^ ^ . | . . . . . |
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Step One: Move F
  1. Push E two tiles west.
  2. Push G two tiles south.
  3. Push F one west, two south, one west.
  4. Push G two tiles back north.
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| . | G | - - - - - | ^ | . . . . . |
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| . E . . . . . . | . . . - - - - ^ | . . . . . |
| . F . . . | D . C B A . > ^ ^ ^ . | . . . . . |
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Step Two: Remove A
  1. Push D one north and three west.
  2. Push B one tile north.
  3. Take A east to the hole.
  4. Push C two tiles west.
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| . | G | - - - - - | ^ | . . . . . |
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| . E . D . . . . | B . . - - - - ^ | . . . . . |
| . F . . . | C . . . . . > . ^ ^ . | . . . . . |
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Step Three: Maneuver C
  1. Push B one south and take it east.
  2. Push D one tile north.
  3. Push C one north and three west.
  4. Push C four east.
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| . | G | - - - - - | ^ | . . . . . |
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| . E . . . . . C | . . . - - - - ^ | . . . . . |
| . F . . . | . . . . . . > . . ^ . | . . . . . |
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Step Four: Finish
  1. Push C one south and take it.
  2. Push E six east and take it the same way.
  3. Push F one north and take it the same way.
  4. Push G two south and take it the same way.
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