Because standalone installations are more lax with extension security, and since you can convert a regular profile to a standalone profile, I'd say to do the following:
Download the Opera installer, launch it, click "options", set "install path" to a folder named "Opera Save" on your desktop, set "install for" to "standalone installation", make sure "Import data from default browser" is unchecked, and install. After that Opera launches, close it and delete everything in the "profile/data" folder in the install folder that's on your desktop.
While your normal Opera is closed, copy all the files and folders in its profile folder to the "data" folder for the standalone installation. Then, launch that Opera. Then, close it and launch it again. Close and open a couple more times for good measure.
If your extensions and their settings remain in tact, copy the whole "Opera save" folder to the other computer or new install of Windows and run that Opera a few times. If your extensions are still in tact, download Opera and install it normally. Then, close it. Then, delete all the files and folders in its profile folder. Then, copy all the files and folders in the "Opera Save/profile/data" folder to the regular Opera's profile folder. Then, start the regular Opera and see if you extensions are still in tact.
However, you're past that now as you can run the old profile files in a standalone installation on the old install. But, in the future, you can try the above. No guarantees that it'll work.
