Hi Kris have you tried this?https://www.my-private-network.co.uk/knowledge-base/apple-related-questions/ipadcache.html
You actually only need a large amount to actually download the update as it will not take up the same amount when loaded.So best thing to do look is look in settings and see what you can delete to give yourself the space or store all your photos in the free amount of cloud or on a hard drive then delete them which will give you the space and then reload them.
A couple more suggestions, though you seem to have tried most things.
1. Make sure your iPad is backed up (locally or on iCloud), and then Restore it, which replaces the whole system. I think this needs to be done by connecting to a computer, ideally a Mac, but you may be able to do it direct (try Settings; General; Reset).
2. If you have a Mac, you can do the update to iOS 8 without having to clear any space: the reason you need I think 5GB if you do it direct is that it needs that space to shuffle the bits around, but releases it again once the install is finished. If you are connected to a Mac it doesn't need this shuffle space.
Once you have iOS 8 installed, you can look at storage by App (Settings; General; Usage), which may help (or may not!)
Have you emptied the Trash and Junk files
I am sorry I can’t help you! I had exactly the same problem and so had another friend of mine.
We deleted just about anything we could and still got the message that we didn’t have enough space left for an update.
Since I wanted to get an iPad Air anyway, I got my daughter to bring me one from Hong Kong (where they are considerably cheaper) with a storage capacity of 128 GB instead of the 16 GB from my old iPad.
I heard that Apple want you to buy a new iPad by simply not letting you update your old one anymore. Have you asked in internet forums? Another option would be to go to an Apple store and explain the problem (I might still do this with my old one).
Good luck and let us know the outcome!