Connect either side of the dipole to the SW antenna input jack and just leave the other side hanging. You can experiment with connecting it to the receiver's ground but I doubt it will make a lot of difference.
It sounds like you're making this a whole lot more difficult than it needs to be. As many have said, you're not transmitting, so just a random length of wire up in a tree (preferably insulated from the tree, but...) is all you need to hear a LOT of signals.
I downloaded the owner's manual for the GS-350DL, which seems to be a newer model. Didn't look any further, so the original manual might be out there somewhere.
It sounds like you're making this a whole lot more difficult than it needs to be. As many have said, you're not transmitting, so just a random length of wire up in a tree (preferably insulated from the tree, but...) is all you need to hear a LOT of signals.
I downloaded the owner's manual for the GS-350DL, which seems to be a newer model. Didn't look any further, so the original manual might be out there somewhere.