From looking at the BOM for the E5 module, many alternate crystals are listed. One of these, Epson FC-135-32.768k-12.5 is listed. This particular oscillator is called out in Table 7 of ST app note AN2867 (Oscillator design guide for …).
Specifically, the gmcrit for this crystal is 2.1312 uA/V. In table 5 of AN2867, the gm of the oscillator and the associated gmcrit is listed in the table. For this crystal, it seems that high drive is required to get the gm_crit_max to be over the gmcrit of the crystal.
The problem is that the sample code uses low drive. This makes the gain margin less than 1 when the app note wants the gain margin > 5.
Is this correct, or am I missing something?