Refrigeration compressors generally have a start up surge. It usually lasts less than a second, but can last longer depending on the system. This includes refrigerators, air conditioners and heat pumps. It is the large current draw that it takes to get the compressor started. Once the compressor is started the current to run it drops significantly.
That being said...
The lower cost method might be to keep the battery or find a smaller one that can still source 100 amps during the start up surge. Put a low cost charger on it so that it is constantly being charged. The charger will source current to charge the battery as well as the low current portion of the duty cycle. The only time the battery will be drained is during the startup surge.
This will be easier if you can measure the duration of the high and low current draws by the refrigerator. This will tell allow you to size both the battery and the charger. The battery must be able to source the 100 amps for the startup and the charger must be able to source enough current to charge the battery between starts and to supply power to the fridge while it is running at low current.
That being said...
The lower cost method might be to keep the battery or find a smaller one that can still source 100 amps during the start up surge. Put a low cost charger on it so that it is constantly being charged. The charger will source current to charge the battery as well as the low current portion of the duty cycle. The only time the battery will be drained is during the startup surge.
This will be easier if you can measure the duration of the high and low current draws by the refrigerator. This will tell allow you to size both the battery and the charger. The battery must be able to source the 100 amps for the startup and the charger must be able to source enough current to charge the battery between starts and to supply power to the fridge while it is running at low current.