Progress made! Turns out ASYD Sys=1, Index 420, bit 1 allows access code using preset dialing. SIP phones only do preset dialing (where you dial all digits before you hit # or otherwise start the call), and looks like with this turned on, I can now dial out, but only if the call doesn't require auth-code. So I'm good on local calls, but long-distance is still a problem....
Actually, never mind...
I was just testing something while typing this: dial the number AND the auth-code before hitting # on the dial-pad. And voilah! It went through.
Looks like problem solved