Wow, that is a serious network. To be quite honest, this is not going to be an easy task. I2C was never really designed for that large of a network. After all it is named Inter-Integrated-Circuit bus (hence I2C). It was really only designed to be used on a single PCB or perhaps between multiple PCBs. However a lot of people have used it for local communications within the same housing, hence why we offer it on our displays.
Some background, I2C is a standard for a multi-drop communications bus developed by Philips (now NXP). You can read more about it here:
While RS422 and RS485 are differential and suitable for long distances due to their noise immunity, I2C is a wired-OR bus that relies on resistors pulling it back up to the high state. With that much cable, you not only have a large amount of capacitance, your topography will lend itself to issues with reflections running up and down the bus.
On the capacitance front, I2C specifications says that there can be no more than 400pF of capacitive loading on the bus. What your describing will most certainly violate that. Ideally I2C would have a single line going from one end being the master through a bunch of slaves to the last slave on the bus having the pull-up resistors. With a trunk/branch topography, that simply is not possible. Your branches are getting close to 10% of the trunk length, which could cause serious signal reflections up and down the bus.
The PDF linked above has some suggestions on using I2C extenders to divide up the bus. With one of those at the junction of every branch along the main trunk, you might be able to get the topography issues straightened out. If your main trunk of 400 feet still violates the 400pF limit, you'll have to look into breaking up the trunk itself with more I2C extenders.
On the cable front, since this isn't a differential signal, you'll need to look into as high quality cable as you can. Properly grounded shielding would also be a very good idea depending on the EMF in your environment.
Bottom line, it will be possible with careful engineering, however it will be quite a challenging task.