I think I found a solution to your problem described by user C Wills in a DPReview Forums post from 2012. I have tried to make a step-by-step recipe of his advice here.

Part one - create an unedited photo to copy all settings but crop factor from:

1. Create an unedited version of any photo in your Lightroom collection with no settings or modifications applied*.
2. Go to the Library Module and select the unedited photo in 1.
3. Select "Copy Settings" (Ctrl + Shift + C) - the "Copy Settings" panel opens.
4. In the panel uncheck the settings you want to keep. So uncheck Crop settings in your case. I usually also uncheck Lens Corrections, Process version and Calibration since I like to keep those settings as well.
5. Press the Copy button in the panel. The panel closes.

Part two - paste the settings from the unedited photo to virtual copies of your photos:

6. Create virtual copies of all the photos you want to reset everything but their edited crop factor (Select the photos - press Ctrl + ')
7. With all the new virtual copies selected (they're selected by default when making the copy) select "Paste settings" (Ctrl + Shift + V)

All settings that you had copied from the unedited photo are now applied to your selected virtual copies. You now have "unedited" versions of your photos with edited crop factor.

*) This explains how to make an unedited version of a photo from an edited version: 1. Create a virtual copy of any photo in your Lightroom collection with the same Process Version as the photos you want to reset (Ctrl + ') 2. Select the new virtual copy, and go to the Develop Module 3. Reset that photo back to it's original state with no changes by selecting pressing the Reset button in the bottom right corner of the right module panels or pressing Ctrl + Shift + R