I still don't understand what you mean by the I2C pull up resistors.
Every sensor, and possibly also the Arduino, has a pullup resistor on each of the I2C lines. They are all in parallel, and that demands far too much current from the I/O lines.
You will have to remove both pullup resistors on at least 13 of the 14 sensors if you insist on this arrangement.
I figured it'd be easier to route all the data through one device, instead of say, 7 Pro Minis.
Obviously, it is not so easy.