Unless this is in a noisy (electrically) environment I don't think you'd need CAT6.
I my lighting systems I use pre-configured CAT5 cables with a PCA9600 I2C bus buffer and this works fine for up to 1MHz. I believe the max on the Arduino's is 400KHz so that would work fine on 20m.
The pull-up resistor configuration in Fig. 9 should work fine. Place the 470 Ohm resistors at each end of the bus. Or use a single 270Ohm pull-up resistor as shown in Fig 12.
The 4.7K on the Arduino side is a save value. The I2C pins for normal (100KHz) and fast mode (400KHz) pins only provide 3mA to discharge the cable(system) capacitance. Thus the limit to 400pF max system capacitance. Assuming a voltage of 5V and a pulp resistor of 1.8K result in a current of 28mA. 4.7K result in a current of 10mA according to Ohm law, so there is room to play.
Here is an excellent Article to the effect of varying pull-up resistors:http://dsscircuits.com/index.php/articles/47-effects-of-varying-i2c-pull-up-resistors
Everything Arduino <->I2C you'll find explained here:http://www.gammon.com.au/forum/?id=10896
In general I am not exactly sure why you chose the P82B715PN. You don't use other bus buffers in your system so thats one advantage that this buffer chip has that you cannot take advantage of in your system and it also does not isolate the bus capacitance which could help. I am thinking that a PCA9600 would be a better choice.
I could provide a schematic and a PCB layout that is breadboard ready.
The small board in the image below between the Ethernet Jack in the front and the Teensy 3 micro controller in the back hosts the PCA9600 I2C buffer chip, the Schottky diode and the necessary pull-up resistors. You'd need two of those little boards. One for each Arduino.