Update: I cleaned the throttle body area with CRC throttle body cleaner. I pushed the start button to the accessory mode and then had my wife depress the gas pedal so that the butterfly valve would open. There was a high pitched squeal while doing this. Quite a bit of brown fluid, as well as some fine dark powder was seen running down as I sprayed. I also wiped out as much of it as I could. The perimeter of the orifice looks quite clean now.
After reassembling all the hose work, I cranked it back up and it didn't want to start for 10 seconds or so. After that, it did crank but the idle was rough for a bit. After a little while, the idle became very smooth, with no fluctuations in rpm.
I then took the car out for a drive. As I began to accelerate, the CEL began flashing and the car ran rough. After this, I let off and coasted down the street for a bit. I was going to go back to the house, but the CEL disappeared. So, I continued the drive.
While driving, it seems that the car has forgotten its engine mapping because it seems to be down on power, as well as not wanting to downshift very well when applying the throttle. It used to downshift aggressively. I drove for around a half hour, and it seemed that the downshifting got better, but still not like it was before.
I'm suspecting, and hoping, that somehow the ECU has lost its memory on acceleration and downshifting. It drives very smoothly, however. It also has a bottle of Seafoam in the gas tank, and it does seem that after I put the Seafoam in the tank, it was down on power. Finally, it is about 80 degrees outside, and I am accustomed to driving with the temps in the 60s here lately, so that might have something to do with it as well.
With regard to my original issue of the car dying when restarting it after it sits for 30-40 minutes, I will have to wait to see how that pans out.
Any thoughts? Thanks for all the tips and info here.