This will require some effort. If possible, you should contact the company that made the board to help you with building the new bootloader to work with the Wiring Framework.
To reprogram that board, you'll need to use the internal RC oscillator (running @ 8MHz) as I think that it has a 14.7456MHz external crystal.
Here are the makefile settings for the .mk file in the booladers/build folder for Wiring. E.g. ATMega128A.mk
atmel-128a-8MHz: HARDWARE = ATmega128A_8MHz
atmel-128a-8MHz: MCU = atmega128a
atmel-128a-8MHz: BOOTLOADER_ADDRESS = 1F800
atmel-128a-8MHz: F_CPU = 8000000
atmel-128a-8MHz: HW_DEFS_H = defs-wiring-v1-mega.h
atmel-128a-8MHz: EXTRACFLAGS = -DBOOT_USART=0 -DBOOT_BAUD_RATE=-57600
mv $(PROJECT).hex $(PROJECT)_$(HARDWARE).hex
Here are the fuses you will need to program onto the ATmega128A:
The fuses will set the '128 to use the internal RC oscillator @ 8MHz.
If you create the ATmega128A.mk file with the above information, and put it into the Wiring bootloaders/build folder, you can run make atmel-128a-8MHz in that folder to create the new bootloader.
You will have to have a version of avr-gcc installed somewhere (I think the board that made the company walked you through how to do that).
Let us know how it goes!