....I start a gentle turn to starboard (maybe 10 degrees) at 2 minutes out, bring it harder at 1 minute out (maybe 20-30 degrees),
I get your drift, but strictly speaking not in compliance with the colregs. Rule 8 states, in part:
(b) Any alteration of course and/or speed to avoid collision shall, if the circumstances of the case admit, be large enough to be readily apparent to another vessel observing visually or by radar; a succession of small alterations of course and/or speed should be avoided.