You need to challenge the startup circuit, which is in a
sense challenging your assumptions. This wants a few
angles exercised. I'd do a very slow transient ramp (PWL
source or pulse w/ long trise) and I'd do a DC sweep, and
insist that both of them produce the same result (a clean
start, and no clinging to the ankles afterward - i.e. the
startup must cease sourcing current into the ptat loop,
otherwise your tempco will be jacked at some process
corner).
If you can break it, you're not done. That's the drill. And
you must try everything you can, to break it.