So, I’ve done a bit of playing around with balance numbers using http://www.samcfuchs.com/ClimbingSimulator/, and it seems that mounting rigidly at a 90 degree angle to the bar makes the bar more level in every single scenario (except if your CoG is above the bar, which always makes the bar less level).
In most reasonable configurations, using rigid 90 degree mounting and a CoG 30 inches below the bar will make the bar between 0.5 and 10 degrees more level. Also important to note that in ANY config (except if your CoG is above the bar, which always makes the bar less level) replacing any robot with an equivalently weighted robot at the same location that has a rigid 90 degree mount will make the bar more level.
NOTE: This may be slightly inaccurate if your mounting point isn’t centered over your COG when your robot is transposed onto a level plane. Also, the mounting angle at the attachment point has to be EXACTLY 90 degrees to never have negative effects, but the angle from the bar to the bottom of the robot can be slightly off 90 degrees due to flex in the metal without ever causing negative effects on the levelness compared to a non-rigid robot.