The IAC would be the first suspect for being gummed up.
Remove it and clean with intake cleaner made for the purpose.
Also clean the inside of the throttle body around the throttle plate area.
A little background on why the motor may stall upon braking is as follows;
The speed sensor tells the PCM what is happening to the road speed by driver action (braking).
This does several things. It unlocks the convertor, shuts down the fuel and keeps the IAC open just enough so the motor won't stall.
As you see, the IAC cannot respond so the motor stalls.
The gum around the throttle plate has limited air flow vs opening angle as well.
Also the PCM has tried to account for the problem by shifting it's tables to some degree. After some drive time, the PCM will return to it's more normal operating table values as you drive.
The IAC is not looked at for much more than an open electrical circuit or malfunction bad enough to cause a code for some other reason like to low an idle speed etc.
The TPS is part of the throttle body operation so is not able to tell much about anyting but it's own travel or electrical circuit.