Original tire was a bias ply (78% profile) 7.15 x 14 inch on a 14 x 5-1/2 inch wheel. You could run chromed reverse wheels with a four inch offset and it would still clear the wheel well with a seven inch wide tire.
Now if you are running a bigger tire and wheel then it is on you to figure out what combination will work. I use this tool to measure the space I have to work with, and to simulate any tire and wheel combination before I pick up the phone to buy anything.
I went down to my local tire store and with masking tape attached to every piece of wire to form a label and a felt tip pen; I wrapped the wire around every tire size I could find to make a tire profile. (I used to buy a lot of tires from "Mo" the manager so he let me wander through the tire warehouse with my collection of coat hangers).
They hung on the wall of my shop for years so that when a customer wanted a wide by huge wheel I could mount my tool on his car or truck and show them where their tire and wheel choice would hit the body.
Two doors down from my shop was an independant collision repair (and I suspect a chop shop), and next to him was "Norm the Sorcerer" a custom bike and van painter (back in days of tradesmen size vans with murals of naked women and dragons on the side). They could open up the wheel well to fit any size tire if they were willing to pay that much, or just buy something that would fit.
All that said disc brakes were offered on your car in 1967. They used the front brakes off of a Corvette on the full size that had a four piston fixed bridge Girling caliper (cast with an AC-Delco logo, but it was a Girling made brake part). The Corvette Rally wheels will clear the brakes and an eight inch wide wheel will fit in the back easily. As will a seven inch wide Corvette Rally wheel up front.