How to delete burst photos stuck in Recently Deleted folder?
How to solve:

Recover everything from 'Recently Deleted'
Go into your Photos, and scroll down to 'Bursts'
Follow these instructions, noting it will be a little more difficult for you since you may be looking at completely blank images rather than actual images (but it will work even for completely blank images, I can confirm this).

The steps to delete an individual burst from Photos are

Go into Photos
Scroll down to 'Bursts'
Select a burst, and press 'Select...'
Click in the center of the screen to pick any photo as the 'Favorite' (it doesn't matter which one since they'll all be deleted in a moment)
Tap 'Done'
Tap 'Keep Only 1 Favorite'
Tap 'Select'
Tap the 1 Favorate photo you chose in Step 6
Tap the trash can to delete it - it's gone!

Repeat the above steps once for every burst you want to delete.