The problem seems to be that the wallet from my old installation of Windows HAS A LAST MODIFIED DATE THAT IS OLDER than the transactions which funded the wallet address in question. Since the backup of the wallet seems to be prior to receiving the BTC, is this why I have no key for this address?
It depends: before HD-wallets, Bitcoin Core used a keypool, which by default stored 100 addresses. Any backup you made, should have the same 100 addresses. When you ran out of addresses, new addresses would be created, but your backup wouldn't know them.
If you deleted your wallet and restored an older backup, it might not have all your private keys. In that case it's impossible to restore.
Did you receive payments to 100+ addresses before this transfer?
Have you written down the seed of your wallet somewhere? Would be much easier to just recover everything using that.
Also, i'm assuming you're using Bitcoin Core?
Bitcoin Core doesn't have a "seed".