Lexus SC430 Stalling Problem

I purchased a used SC430 with 95,000 miles in June of 2011. During the summer, it began to stall, similar to vapor lock, during acceleration and even with steady driving. It also stalls occasionally upon initial start from a stop. This has continued, regardless of weather, and it is intermittent. I have found that it can be overcome by releasing the gas pedal for a few seconds, then depressing it again. The stalling has never caused the engine to stop completely and idle is fine at all times. I would say the frequency of this hesitation averages about six times during a 20 minute drive. My wife drove it to our new home in April of 2012. I forgot to mention the stalling to her, and she said it caused her to drive quite some distance at 45 mph even with the accelerator almost floored. I suggested taking her foot off of the accelerator for a few seconds, and this also worked for her. I tried different fuel octanes and used a can of water remover, all with no change to the stalling. I would very much appreciate suggestions on what might cause this and how to remedy it. June 2011 - Owned vehicle for a month and stalling started. June 2012 - Stalling simply disappeared and engine operation returned to normal although nothing was done. February 2013 - Stalling returned. Suggestions which have been Offered: 1. Check the air filter and replace it, if needed. 2. Clean the throttle body. 3. Check MAF sensor and TPS (throttle position sensor readings). The(TPS) is inside the throttle body that controls your acceleration. If it fails, you'll definitely know, as the vehicle won't accelerate properly (stalls, works okay sometimes, etc.). 4. The Idle Air Control Valve (IAC) can cause of poor idle and stalling. The IAC can be repaired by replacing a couple of cheap bearings. 5. Change the PCV valve since it can cause stalling. 6. Check fuel pressure since it could be a bad fuel pump. 7. Change the fuel filter. Yet they are almost lifetime filters and are difficult to change.