That's larger than I would want, and you may see
the tempco improve by changing the bias setpoint
lower.
You kind of have to "take what you get" for voltage,
if you want tempco right. Some process' diodes may
give you 1.25V while another's gives you 1.21 for
the "magic" voltage. You can tweak with number of
diodes (ratio) and so on. But if you reall, really need
dead-nuts 1.250V you may have to do things like a
buffered output w/ divider, or something. Usually for
a standard analog cell design, you just document what
the voltage happens to be, with flat TC, and use that
value in setting up other feedback ratios, etc.
CMOS bandgaps can be run nelow 10uA though for my
uses I prefer maybe 50uA, this gives a little better
matching (further away from a variable SOI leakage
floor, etc.) and tightness of distribution.