I agree it would will be very difficult to pull a new cable. Instead I'd pull off the entire roof antenna mount plate and see if there is enough coax exposed or can some spare wire can be pulled enough to crimp a new connector on the end and then add a new section beyond that point. Otherwise I think the best bet would be run a new cable across the roof and use a cable entry plate from Winegard, such as Winegard CE-1000 Plate Cbl Entry Single
. Many sources for the same part. The entry plate would need to be well sealed with a self leveling sealant. Drill a hole straight down into the TV compartment. You could use some self leveling sealant and place a few dabs of it along the cable to keep it from flapping about on the roof deck. Alternatively, you can use a strip of roof repair tape to hold it in place.
Having pulled many miles of computer cable, its amazing to me people don't leave enough spare wire at the ends to make repairs when needed. A few feet of cable is cheap and is light enough, but the factories try to save everywhere to our regret.