You know that I'm not an aeronautical engineer, but I have a Classic Mustang buddy who works for Boeing in Bellingham, Washington who is and in discussing the airflow over, around, and under a Healey with him, he pointed out several things.
The rear of nearly all cars have a very thin layer of air, called the boundry layer, that flows UP and forward under the main rush of air flowing down and rearward over the trunk lid. In the Healey, this may be exagerrated because of the rounded back end and long sloping trunk.
At speed, because of the air flowing up over the bonnet, then up over and around the ends of the windshield, the entire cockpit is a low pressure area.
Depending on the vehicle speed, wind direction and speed, it is possible that low pressure of the cockpit area is pulling the boundry layer all the way up the trunk lid and into the cockpit.
One reason that many modern cars have have a small "lip" spoiler on the trunk lid is to help merge the air flow over the car into the merged airflow at the rear of the car and prevent the boundry layer from advancing farther forward.
If your exhaust pipe is angled upward and/or too short, you might be introducing exhaust fumes into the boundry layer which then get sucked up to the cockpit.
Many performance cars (Porsche, Crossfire) have a small, servo driven spoiler, that raises at speed to disrupt and stop the boundry layer.
I'd lower the angle and/or lengthen pipe so that the tip protrudes more into the airflow from over and under the car and farther from the area that feeds the boundry layer.
Please let us know what you do and what happens.
Tim