[Al Skierkiewicz]

Starting off with the bridge rectifier discussion...
Batteries do not need to use diodes when in series. The current SLA battery is six 2 volt cells in series with no diodes. Use diodes (a single diode in series with each battery, not a bridge) when paralleling batteries so that the batteries don't self discharge each other. Diodes are available from RV stores or use Schotky diodes that have a very low forward voltage drop.
Other battery types can give significant currents in the same package size as our current SLA but there are drawbacks like cost, type of charger, and damage potential. And yes, NiCad cells are available that are larger than normal battery sizes.