how to modify a taper charger of lead-acid batteries to be a constant current charger?
Your dumb charger is just providing a slightly regulated voltage.  It works due to the combined resistances of the charger and battery limiting the current.  As the battery voltage gets close to the charger, the voltage potential is less.  So with a fixed resistance, the current drops.

I doubt that you can modify your current charger to push 38 A up to 14.4 V.  This could only happen if the combined resistances and voltage difference allow sufficient current flow.  

Most likely you will need a higher voltage source and then circuitry to make a constant current source to provide a fixed amperage.  Shutting it off can be done with a simple comparator circuit.  Put a 10k trimmer pot across the battery voltage and run it into a comparator along with voltage from a zener regulator.  Then you just adjust the voltage divider from the pot till it trips at the correct battery voltage.  Use that to turn off a high current MOSFET or something similar.  (Might use the same MOSFET to control the constant current.)