Ultracapacitors as a battery; how long will they last?
Let's look at a simple analysis first. The basic equation relating current and voltage is $$\frac{dV}{dt} = \frac{i}{C} $$ where i is in amps and C is in farads. For a current of .03 amps and 58.33 farads $$\frac{dV}{dt} = 5.14 x 10^{-4} $$ so in one hour $$\Delta V = 1.85\text{ volts}$$ Since 14.4 minus 11.5 equals 2.9 volts, your ultra caps will last about $$\Delta t = \frac{2.9}{1.85} = 1.57\text{ hours}$$

This is so short a period that you simply don't need to worry about self-discharge currents.

EDIT - Along the same lines, you need to take a look at the load on a car battery. The big-ticket item is starting. Starting loads are typically 100 to 200 amps.

For a current of 100 amps (and this is best-case, remember. Starting in cold temperatures takes rather more.) we find $$\frac{dV}{dt} = 1.71 $$ and for a 2.9 volt drop, $$\Delta t = \frac{2.9}{1.71} = 1.69\text{ seconds}$$
For 200 amps, of course, the time is half that, or about 0.85 seconds.

So you might want to reconsider using caps (ultra or otherwise) for a car battery replacement. Also, just for fun, you need to check the spec sheet for the maximum current which can be drawn from an ultracap without damaging it.