You do realize their mantle gets about the size of a volleyball and their arms get about 60 inches long (5 feet) right?
300 gallons isn't going to cut it for very long. They are very active and being couped up in that size of a tank is not going to be healthy for it. Once it gets about 8 months old it's going to start getting very restless... and wrestling that large of an octopus back into a tank is not my idea of fun. Plus consider how much an octopus that large is going to eat. The GPO at the Dallas Aquarium was about the size of a full grown O. cyanea last time I saw it and they were feeding it several medium sized fish in one meal. We're not talking hermits and snails here. We're talking 6-7 inch fish. You're going to be spending a fortune at the seafood section of your grocery store. Plus water changes... the unholy mess one of those would make in a 300 gallon is unthinkable.
Why not find an O. vulgaris? One of them would be fantastic in a 300 gallon, and not outgrow the 55 so fast while you're cycling the 300.
I hate to be discouraging. I really, really do. But realistically it's just not a good plan long-term. They are an awesome species. I don't blame you for wanting one at all. If I had the money and a spare bedroom I could turn into a giant tank I would keep one. But my desire to keep one is trumped by my lack of the ability to maintain the necessary environment.
They are diurnal and live two years. I've kept several and in captivity they usually do not get much more than 2-3 kilos, but that is going to take at least your 300 gal tank. Still, because of their personality and activity pattern, if you can get a small one, they do well in a large aquarium.