about bandgap design
That kind of tempco may not be attainable without some
curvature correction, and c.c. is a first class bitch to get
right (cubic response magnifies all the "make" tolerances
even worse than the parabolic plain bandgap).
The ultra-precision, ultra-stable ones all seem to be using
a temperature sensor, digitized, and a compensation map
in ROM/EEPROM to get an arbitrary dead-nuts correction.
10mV may be on the edge of doable, but I would expect
the model accuracy alone to be a significant issue with
little hope of resolving it beforehand. You might find you
have to take your own diode and resistor data and fit
your own, possibly veriloga models (simple tc1, tc2 may
not suffice). This usually takes an initial pass with the
best guess bandgap plus key elements to extract better
models from, and a tweak pass through fab.
Unless you're a genius at guessing and have great karma.