You could try playing with
our favorite carbonation table along with
the only beer line length calculator worth using to see what your options are.
For instance, assume your preferred dispensing temperature is 40°F and you like a middle of the road carbonation level of 2.5 volumes.
Using the table, the CO2 pressure you'd use is 12psi.
Plug that 12 psi into Mike's calculator, and set the vertical distance to the net gain in height from the center of the kegs to the faucet tip.
I'm guessing the "6 feet to the ceiling" is from the top of your keezer, so there's probably a couple of feet missing from that metric.
At the other end the line is actually dropping; you want to subtract that drop from the rise at the keezer end to get the net rise.
I'm going to guess that net is 5 feet, so plug that into Mike's calculator.
If you leave the line ID set to .1875", the calculated result is 8.74 feet - obviously way short.
But change the line ID to .250", leaving everything else alone, and the result is 34.56 feet - which could be a perfect solution.
So, tweak the temperature and carbonation level you prefer first, get the resulting CO2 pressure to use, plug that into Mike's calculator and make any other needed adjustments (that net rise factor, for instance) and you can see what results you get...
hth
Cheers!