I came kinda late to this particular party, but I know how to diagnose engine problems the old fashioned way. The most computerized bit in my previous car was the turn signal relay...
I didn't read the whole thing, but the first post told me just about everything I need to know. You have to think of it in terms of systems and symptoms. Your problems exist upon heavy loads, and "studder" is spelled "stutter" (had to toss that one in there). Backfires typically occur from one of three sources, overly rich mixture, overly lean mixture, and off timing.
If it were overly rich and backfiring, you'd have a CEL from the cat being bad. Catalyzed exhaust systems require additional fuel to burn in the cat and keep it working. Too much fuel (or oil) will burn out the cat and you have a CEL. Since you don't have a constant CEL, you're not too rich. Additionally, the stutter indicates it's probably not rich because it would have to be INSANELY rich to cause that and you'd smell gas in your exhaust (also, cat would be burned out).
Timing is controlled by your ECU, so you don't have to worry too much about things from that end. Your coil packs could be bad (you don't feel they are, but electronic things don't always go bad in obvious ways). You've changed your spark plugs, which would take care of a rich condition caused by a missed spark causing unburnt fuel to enter the exhaust system and cause a backfire. Still, if a coil pack were bad you'd have the condition at times other than just under heavy load.
This leaves a lean condition, which fits all of your systems. A mixture that is too lean won't burn correctly (there's your stutter) and may not be burned in the cat, then backfire in the muffler (slowing of exhaust gases causes an accumulation of fuel which would then ignite when the hot gases from what is correctly burned in the cat from the next cylinder firing). Things would be fine under normal loads if a particular injector were only able to squirt enough fuel in all but the most demanding of loads.
So we're looking firmly at the fuel system for a cause of a lean condition. The fuel systems includes the tank (no effect here), fuel filter (replaced), fuel pump (you ruled it out, but I didn't see why), injectors (likely), MAF (no associated code), O2 (no associated code), TPS (no associated code), and ECU (not likely).
I assume that since you said you use injector cleaner regularly you've done it here (bad gas, sitting for a while, etc. can gum an injector quickly) and they're clean. That means at least one is bad. Odds are there's only one bad (two would be unlikely enough to rule it out statistically).
Finally, here's how to figure out which one! It's probably not going to make you feel warm and fuzzy, but stay with me. It sounds like it's doing it now as a function of RPM (a more severe condition than if it were just doing it under load but just further along the same spectrum), so that actually makes things even easier. If you manipulate the throttle by hand from the engine compartment you'll be able to rev it up to the point of stutter. Now comes the fun part: shut off the engine and disconnect a spark plug wire (otherwise it's a fairly unpleasant shock; not lethal, but definitely not something you'd likely care to repeat). Start is back up and see if you can get it to start with one spark plug wire disconnected. It won't like it, but it should still run. Now rev it. If it dies or runs even worse at the 2500 RPM point, the cylinder with the pulled plug is NOT at fault. If it stutters like it has been, there's your culprit. It's not the nicest thing in the world to do to your cat, but if you're quick cycling through, it won't be as bad as maintaining the status quo. Once you've figured out which injector is at fault, replace that one and you're good.
