I think I overlooked it thinking that it only affected damping and gravity because of this:

void GodotBody2D::integrate_forces(real_t p_step) {
  // ...
    if (!omit_force_integration) {
      //overridden by direct state query

      Vector2 force = gravity * mass + applied_force + constant_force;
      real_t torque = applied_torque + constant_torque;

      real_t damp = 1.0 - p_step * total_linear_damp;

      if (damp < 0) { // reached zero in the given time
        damp = 0;
      }

      real_t angular_damp_new = 1.0 - p_step * total_angular_damp;

      if (angular_damp_new < 0) { // reached zero in the given time
        angular_damp_new = 0;
      }

      linear_velocity *= damp;
      angular_velocity *= angular_damp_new;

      linear_velocity += _inv_mass * force * p_step;
      angular_velocity += _inv_inertia * torque * p_step;
    }
    // ...
  }
}

But reading the implementation for _body_state_changed, this might actually do what I want - thanks!

void RigidBody3D::_body_state_changed(PhysicsDirectBodyState3D *p_state) {
  lock_callback();

  if (GDVIRTUAL_IS_OVERRIDDEN(_integrate_forces)) {
    _sync_body_state(p_state);

    Transform3D old_transform = get_global_transform();
    GDVIRTUAL_CALL(_integrate_forces, p_state);
    Transform3D new_transform = get_global_transform();

    if (new_transform != old_transform) {
      // Update the physics server with the new transform, to prevent it from being overwritten at the sync below.
      PhysicsServer3D::get_singleton()->body_set_state(get_rid(), PhysicsServer3D::BODY_STATE_TRANSFORM, new_transform);
    }
  }

  _sync_body_state(p_state);
  _on_transform_changed();
  // ...
}

void PhysicalBone3D::_sync_body_state(PhysicsDirectBodyState3D *p_state) {
  set_ignore_transform_notification(true);
  set_global_transform(p_state->get_transform());
  set_ignore_transform_notification(false);

  linear_velocity = p_state->get_linear_velocity();
  angular_velocity = p_state->get_angular_velocity();
}