"But how to work around the write cycle limit of eeproms?"

First, minimize the number of times you have to change a particular location.

As a crude example, using gray code counting down, you can make several counts without erasing. Then use the count to point to different areas of the eeprom to spread out the data.

Or, write the data with a timestamp. Each time, write the packet after the last used address. On power up, search for the last valid packet.