RTC chip not happy with xtal waveform
The new chip is probably optimized for very low power.  It may not have the drive level to get enough amplitude thru a 12 pF crystal when the proper load caps are used.

However, you say you see a signal when looking at one of the crystal pins with a scope.  If you see the expected frequency, then the oscillator is working when you are looking at it.  This may be because the scope probe capacitance is adding the phase shift needed for the loop gain to be above 1 at the crystal frequency.  

If this is what is happening, then there should be two clues.  First, the RTC will work while you're holding the scope probe on the crystal pin.  Second, it will only work when the scope probe is on the oscillator input, not the output.  It is the phase shift caused by the extra capacitance on the crystal output that allows for oscillation.

Either way, there really should be a little capacitance on the crystal output (the oscillator input).  Kludge on a 10-12 pF cap between the crystal output and ground for now.  When you re-design the board, include pads for a cap on each side of the crystal, and get a crystal rated for the 6-9 pF you say the chip is intended for.