I found an $8.76 solution that solves the iPad charging problems.
It doesn't change the issues with the extreme heat levels, but it does allow me to run at 100% brightness using any app I've tried so far and maintain a fully charged 100% plug icon indefinitely (or at least for the five or so hours it's been plugged in and in use.). Oddly enough, it is a 10W 2.0A charger vs. Apple's 2.1A charger. It also has a 6 ft cord but the main difference lies in its hardwired connection to a durable, locking dock plug, vs. Apple's plug-in USB port charger. This Monoprice one surely is better, and Apple would be wise to study it and make one just like it for the new iPad. This leads me to believe part of the fault lies with the Apple charger, and the other obviously is that the iPad draws more power in some instances than the charger can handle but I've yet to encounter that situation with this new charger. It also charges the iPad faster.
Thank you Monoprice. My gamble paid off.
P.S. It is a certified "Made for iPod, iPhone, iPad" product so don't have any reservations about using it. When I have some spare time I plan on taking one to the local Apple store to show them how much better it functions and maybe they can pass it up the chain.Edited by IPodPJ - 4/18/12 at 2:27am