If I was a smart___s, I would tell you to swap the engine with an electric motor. But... I won't do that.
From my own experience even the best sound insulated car will become loud inside with a loud exhaust. So the exhaust will be the best place to work to solve the problem. You need a quieter OEM type muffler, and an exhaust pipe that exits at the rear bumper. Of course that takes a lot of fun out of the car, but that is the sacrifice we have to make to please our non-motorhead family members.
You can put in dynamat type insulation on the floor and behind the interior panels but that is only a very small help for a lot of work and expense. If you haven't already done so, sealing off the trunk from the passenger compartment will make a lot of difference. And don't forget to close off and insulate the opening behind the back seat, since a LOT of noise will come through the seat itself.
There is little to be done with the wind noise, since these 50 year old cars were just are not very aerodynamic and have lots of places on the body the wind will whistle over, such as the rain gutters. You can get new door and window gasket rubber and make sure the doors are adjusted to close tightly and that will help, but only a little. You could test this by temporary putting duct tape on all the gaps and then going out for a drive to see if the improvement is worth the effort. Sound insulation on the bottom of the hood can be a significant help since a lot of sound will come in through the cowl vent. You could try taping off the cowl as well to test that.
Good luck and be sure to let us know if the dog approves of your changes. Inquiring minds want to know.