You're correct that when you increase energy you also increase momentum. But, when using the same bow and same draw weight, you can only slightly increase energy while really loading up on momentum. Doubling arrow weight will only gain a couple of foot pounds of energy (in theory) but it will double the arrow's momentum.
So lets crunch some numbers. A bow that is throwing a 350 grain arrow 300 ft/sec calculates to be 70 ft/lbs KE and 0.47 pound seconds momentum. Now lets double the arrow weight to 700 grains and shoot it. Assuming 100 grains of virtual mass the new result is a 700 grain arrow flying at 225 ft/sec. That's 78.7 ft/lbs ke and 0.70 pound seconds momentum. So the heavier arrow has given us a 12.5% increase in KE and a 50% (not 100% like you said) in momentum. O.K. so what does that mean? Well if you agree that the heavier arrow will penetrate more it means that in this example a 12.5% increase in KE or a 50% increase in momentum (take your pick) resulted in precisely the same increase in penetration.
It's just like I said in my first post...
"If you want to attribute the increased penetration to the increase in KE that's fine. If you want to attribute it to the increase in momentum that's fine too. KE and momentum are merely the result of calculations based on the measureable quantities of arrow velocity and mass. From a given bow, the facts are quite simple. If you put on a heavier arrow, the veolocity goes down and both the KE and momentum increase thereby resulting in greater penetration. "
The relative percentage that each change is irrelevant.
Art, I'm getting a strange de ja vu feeling...