Blademan ST2 no longer is available from the App store – so even if newer iPads were purchased ST2 and 3 couldn’t be downloaded from the App store – to be on the same device.
You can always install version 2 on a new iPad. Look in the "Purchases" section of the App Store. You will find it there and can install from there. If you purchased an app, you will always be able to install it even if it was removed from the App Store.
Your second approach could work if you have properly tagged audio files in iTunes. But in the case that they are not tagged with title and artist, the migration will fail.
So, best way is to install version 2 on the new iPad, restore a backup in version 2, make sure everything runs and then create a new backup and migrate this into version 3.