Couple questions:
-If this isn't showing up anywhere (blockchain.info, for example) where did it come from? Could it be an intentional double-spend just to mess with me?
If you got the wallet.dat from somewhere else, someone could have modified the wallet.dat to display transactions that has never existed before.
-can this transaction be rebroadcasted if the network has no record of it?
Yes. However, if your transaction does not reference to an unspent output, the network will not relay the transaction at all.
-do I need to have the entire blockchain downloaded to get my client to rebroadcast this transaction?
No. As long as the nodes can see and verify the validity of the transaction (inputs, signature etc), you can rebroadcast it using any online tool.
Either way as this (probably?) doesn't have any fees with it and since it is old and no other nodes I've checked see it, should I run as my own full node and rebroadcast and attempt to CPFP? I'm not quite familiar with this stuff, but if this was a valid transaction and the funds are still sitting there this seems like the only option, yes?
No. You cannot use CPFP if the transaction cannot be found, there is simply no transaction for your CPFP transaction to reference to.