this is a difficult question to answer as there are a TON of factors that will affect the gar's growth. first off, captive gator gars in the typical aquarium setting of a hobbyist's home won't get to 7-8' like in the wild.
if you are starting off the fish in an aquarium and moving it up step by step, then it will also probably acquire some stunting along the way just due to basic aquarium dynamics compared to the wild. if you were to put it directly into the pond with a bunch of feeders, then you would be looking at closer to maximum captive growth rates (similar to what we see in aquaculture ponds, etc).
if you are starting it off in a tank, even for the first year, then your 4.5' wide tank would likely be big enough. if you are starting it off in the pond, then it would last you quite a while, but there is a slim chance that the gar may actually do better in a larger enclosure down the line.
i would increase the width of the tank as much as possible and go with that setup, but also consider how you are raising the fish in early life (tank, pond, etc) as this has major weight in how large the gar will get later down the line--
--solomon