Do you get a different origin when you re-home after a power failure? If so, it might be helpful to make a divot with your tool when you're first starting out that's at a known position, off the part that's going to be carved away. That way, when you come back you can move the tool so it's in the divot you made, and you can put the numbers back into the DRO boxes. Once the numbers are restored to the ones you recorded originally, you can move the tool so it's at the place it stopped when the power went out. The DROs should give you a readout that's pretty close to the location last commanded.
If you're using Windows, you can edit your G-code in Notepad, which doesn't add any extra characters or formatting. Use the "find" command to skip to the line which corresponds to the place the tool stopped, like X54.456 Y33.567 (You might want to leave out the last digit or two, and check the Z axis values, in case it's been there more than once). When you're sure you've found the right place, select and delete all the G-code above that, leaving out the initial string up to the M command that starts the spindle, and insert a command like G00 Z 3.500 X 54.456 Y33.567 to send it to the place it stopped without cutting a trench through everything that's in the way.