Open Port 8333 is only necessary if you plan to contribute to Bitcoin Network or actually running a full node.
Besides, to accept incoming connections on testnet you have to open the default port 18333 not 8333.
@OP, You don't have to enable incoming connections to be able to broadcast a transaction.
Ok, that's good to know. Any idea what would cause my node to be able to receive tesnet transactions but not be able to propagate its own?
BitMaxz: I have core configuring to run in Testnet and it shows this when I run $ bitcoin-cli printtoconsole. These are indeed tesnet coins I'm trying to send to a testnet address.