Tri-bars/Aerobars on Mountain Bikes
The main reason that aerobars may have an advantage over flat or road bars is that they are designed so that your main support mechanism is skeletal, rather than muscular. The longer the distance, the more this will hold true.



This picture is of a top triathlete. Note that the forearms are almost parallel, and the upper arms are at a 90 degree angle. This allows the main support for the upper body to rest on the bone structure, with minimal muscle involvement. (Stadler was an Ironman distance triathlete, bike segment of 112 miles). 

While you may see variations on this, it is a general truism that the longer the race, the more comfort trumps aerodynamics, and vice versa (Short races aerodynamics trumps comfort.)

Many of the ultra mountain bike competitors set up their rides similarly, and have "wrap" style aerobars that allow them multiple different hand positions for control, as well as the resting position where their arm muscles don't have to do the work for support.

That all being said, I would point out that many riders go much further than 40 miles with no pain at all. This would suggest to me that your fit is not correct, or that you are not in shape enough for a 40 mile ride yet. Tailbone pain is (usually) a bad saddle and fit, and the rest is also easily attributable to fit. Aerobars will not be a magic cureall for an improperly fitted bike