This solution is tested and verified to work.
Into the Middle
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| . . ^ ^ . . . . | . . . . . . |
| . . - - . . . . | . . 0 . 0 . |
- - ^ | < . . . . | . 0 . 0 . . |
| ^ - - - - - - - - - . - - . |
| . . ^ ^ ^ ^ ^ ^ . . . | | . |
| . . - - - - - - . 0 0 - - . - -
- - - - | . 0 . . . . > |
- - - . - - - - . - -
| . 0 . 0 . . . . |
| . . 0 . - - - - -
- - . . . |
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Label the Boulders
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| . . ^ ^ . . . . | . . . . . . |
| . . - - . . . . | . . A . C . |
- - ^ | < . . . . | . B . D . . |
| ^ - - - - - - - - - . - - . |
| . . ^ ^ ^ ^ ^ ^ . . . | | . |
| . . - - - - - - . F E - - . - -
- - - - | . G . . . . > |
- - - . - - - - . - -
| . H . K . . . . |
| . . J . - - - - -
- - . . . |
- - - - -

Step One: Gain Access
  1. Push A one tile west.
  2. Push D one tile east.
  3. Push G two tiles east.
  4. Push E four tiles north.
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| . . ^ ^ . . . . | . . . . . . |
| . . - - . . . . | . A E . C . |
- - ^ | < . . . . | . B . . D . |
| ^ - - - - - - - - - . - - . |
| . . ^ ^ ^ ^ ^ ^ . . . | | . |
| . . - - - - - - . F . - - . - -
- - - - | . . . G . . > |
- - - . - - - - . - -
| . H . K . . . . |
| . . J . - - - - -
- - . . . |
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Step Two: Lower End
  1. Take F first, to get it out of the way.
  2. Push K one tile east, and take J next.
  3. Push K two tiles west and take it.
  4. Push H one tile east and take it.
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| . . ^ ^ . . . . | . . . . . . |
| . . - - . . . . | . A E . C . |
- - ^ | < . . . . | . B . . D . |
| ^ - - - - - - - - - . - - . |
| . . ^ ^ . . . . . . . | | . |
| . . - - - - - - . . . - - . - -
- - - - | . . . G . . > |
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Step Three: Finish
  1. Push G three tiles west and take it.
  2. Push E five south, 2 west, and take it.
  3. Push A one east; take it the same way.
  4. Take B the same way, then C, then D.
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- - . | < . . . . | . . . . . . |
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| . . . . . . . . . . . | | . |
| . . - - - - - - . . . - - . - -
- - - - | . . . . . . > |
- - - . - - - - . - -
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- - . . . |
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