Possibly connect second charger to Lithium Iron Phosphate battery
3.4V per cell (13.6V on a 4 cell battery) gets you more than 90% charged
3.65V per cell (14.2V on a 4 cell battery) is also acceptable, but only gets another 10% energy into the battery.
You can probably just connect the LiFePo4 battery in place of the lead acid battery and get acceptable performance.  staying below 100% charge will probably result in a longer life for the battery.