Sorry Jon, but I don't see how you can "...moderate the throttle and THEN let go of the brakes".
In a manual, your left foot is normally only on the clutch pedal or not engaged. Your right foot would be on the throttle or the brake pedal unless as Dave says, you "heel and toe" - but you can't do that with most cars let alone Jeeps and Buicks. There are some "racers" who also left-foot brake but I somehow doubt you'd go to that extent with a Buick or Jeep and in any case, if your left foot is off the clutch and on the brake, you won't be able to moderate the throttle effectively because the clutch is fully released and you'll stall the engine if you try to feather the throttle at the speeds you need to affect a slow hill start.
The problem with not using the handbrake is that there is always some roll-back caused by the time lag between your right foot leaving the brake pedal to apply the throttle. With a heavy car on a steep hill, the rollback can be a few inches if you're not fast enough. Not everyone is - that's why the Brits fail people who don't use the handbrake - it's the sensible and safe thing to do. Everything else is bravura.
What kind of Buick was it that had a manual transmission?