How can I go about attempting to get my transaction finalized?
It seems the transaction is finalised. Its just that your wallet doesn't know about it.
Checking the transaction on the ledger, however, shows that it's been confirmed and completed.
I assume this means you have checked the Transaction-ID against several different Blockchain explorers and they all show the Transaction as having more than six confirmations.
In this case you need to do as Pieter Wuille suggested. Create a new wallet, using different software. Either import the private-key or sweep the private-key into the new wallet. There are important implications of these two approaches. People mostly recommend sweeping as safer for most folk.
Before it can show the correct balance, the new wallet may need to synchronise with the network (depending on whether you choose a full-node or lightweight wallet), if so this may take from a few days to a week or more.