Hold on. I think you may be overlooking something. I used adalite.io to go through this process and when I restored my ITN wallet, the rewards amount was not equal to the balance of the wallet if I recall correctly. They are 2 different things, rewards and balance.
You ought to be able to restore the ITN wallet, which will indeed have 0 ADA balance (if I remember correctly). You ought to then “redeem” your ITN rewards on that wallet (you should be able to see the amount of rewards!), which will after success then show the balance of your ITN rewards instead of 0. It was necessary on adalite.io to fund the ITN wallet with 1 or 2 ADA to pay for the redemption transaction. After that I was able to send the ITN reward wallet balance to a Shelley wallet of my choosing.
So, don’t panic and give it another go. I can’t help with Daedalus as the process is driven a bit differently.