I had the same issue with my 1950 COE and 8 foot garage door. I researched this issue carefully (but apparently not carefully enough) and when I arrived with my COE on the trailer, discovered that I forgot about those TALL gorgeous cab marker lights on top!! Even after removing them, I discovered that the cab rose as I removed items in the process of dissassembly.
As C. Andyman suggested you could remove the wheels and place the drums on dollies, but that is not practical for a running truck that you want to move in and out routinely. Or as Spanky suggested, you could let the air out of the front tires to get the truck in the garage, but if you have the original split rims, you don't want to be airing up your tires with low low pressure without a cage or other safety precautions (again, not practical for routine use).
Weight (or lack thereof) on the front axle will vary the height of the truck, so we cannot give you a precise answer. I ended up raising the door 6 inches, which was a big construction project and I had to add panels and longer vertical tracks on the door itself.
Bottom line is that it may, or may not work; it's that close.
