Sounds like ur rad. is not mounted up flush w. the cradle to me. I have a 2 row w/ 1 1/4 tubes, and have more room than that, and I know a 68 barracuda is no bigger than a darts engine bay.
If yur not against the cradle , cut the mounting system off , and have 4 brakets welded/heliarced/ soldiered, on that will make it sit flush.Either that or u have the engine mounted forward from stock. Did unused the trans mount as a guide to installing it ?