The problem here is that by unchecking the "Treat JPEG files next to raw files as separate photos" option is that LR copies both RAW+JPEG to the destination drive, but IMPORTS only the RAW into LR. The JPEG files are not part of the LR database, and therefore there is no way to access or manage them from LR.

However, there is a better way to handle this, and that involves importing the RAW+JPEG into LR, but then instructing LR to reduce the clutter, while keeping the JPEG manageable by STACKING the RAW+JPEG.

So what you need to do is:

1. Check the box that reads "Treat JPEG files next to raw files as separate photos" which will import both RAW and JPEG
2. Import RAW+JPEG into LR
3. Select all the images you imported
4. Choose Photo>Stacking>Auto Stack by Capture Time
5. Move the slider to 0. (the images were captured at exactly the same time)

This will then create a stack of each RAW+JPEG combo file, with the JPEG underneath the RAW. In order to choose just the JPEG, simply Filter on File Type: JPEG

Export as normal. If you haven't edited the JPEG, then LR will simply export the JPEG as is (it will go very fast).