Unfortunately, the change address is completely independent from your first address.
After you have imported the private key into core and sent the transaction (without manually set the change address to your first address), core automatically used a change address from the keypool (generated independently from core).
The only place where this private key is/was stored is the wallet.dat file from core
There is no other way of retrieving the private key (which, by the way, is independent from the address type (P2PKH / P2SH)).
This is a common mistake people do with paper wallets. I am sorry for your loss, but if you can't somehow recover your wallet file, you can't recover your funds.
After wiping your hard drive, did you further use it ?
If you didn't use it too much, there is still a chance that the file is recoverable.
Files do not really get 'deleted', the storage is being 'released' instead. As long as no other data is being written onto that position, it is still accessible.
If you believe that there might still be a chance of retrieving the file, immediately stop using the hard drive and make an image of it (to use recovery software on it; never use it on the original drive).