DS1307 issue

[Art]

I wonder if the pic could be driven by the 32KHz crystal directly,
then you'd only have to use a 1:1 timer to count 15 bit overflow, and that's a second.

Melanie's Easy and accurate Clocks works, does the PCB have the I2C pullup resistors,
and if so, have you turned off weak pullups on the chip?