The battery, between 17.6V full and 12V empty indeed averages at 14.8V and thats a little high for the average car.
I wouldn't mind modifying my alternator to charge to 16 volts instead of 14, running a slightly higher voltage would also increase the performance of the fuel pump and other components, my only worry would be the lightbulbs, though those are cheap, easy to replace, and I could always hook up a dc-dc converter for stuff that really doesn't like 16V.
3 lihv cells (13v full) is just a little bit too low, unless I modify the alternator to put out less than the full 14+ volt, which would then further reduce the power going to the fuel pump, which in my application would be bad, not better.
LiFePO4 is a good straight swap for a car battery, but they're either pricy or not very good so you need more of them in parallel and then they're still pricy, or you need a cap bank thats pretty pricy too.
Oh, and balancing would either be done by just balance-charging it every now-and-then, or by building a little balancing board to permanently connect.