Well, you shouldn't have touched that screw, lol. Sure screwing it in further is going to increase you idle. You have just opened the throttle plate by screwing it in. But now you have thrown off the minimum air setting for the engine. That screw is set from the factory to a calibrated position that lets in a certain amount of air when the throttle body is closed. The computer's programming is based on this calibration. Now that you have altered it, you will be letting in more air than you are supposed to be and you will have a tendency to run lean. The fuel trim tables in your computer are all going to end up changing and your injectors are going to have a longer duty cycle than they should have. Your engine may very well run fine, but the computer isn't going to be running on its optimal programming mode.
Now about your thoughts of the IAC. If the IAC was indeed "weak" (this would mean that the solenoid is essentially broken) it wouldn't work right at all. Even under no vacuum conditions, if the PCM were to specify a certain duty cycle for the IAC, it would be completely incorrect and your idle would be totally erratic.
You really need to fix the real problem of the idle for everything to be perfect. When you replaced the IAC, did you reset the computer so it can relearn everything? Something that simple could be the solution to your problem. The fact is that throttle return screw needs to be in its calibrated position, and the idle of your engine should noticeably change or the engine should stall when it is idling and you unplug the IAC. In addition, your MAF sensor should be working properly to correctly measure the incoming air charge. Adjusting that screw may get you by, but it's not the cause of the problem unless it was previously tampered with and for some reason was backed off from where it should have been, but that's an unlikely case.