Popping decel is a sure sign that the stock ECU is still injecting fuel on decel.
Normally, the TPS should signal the stock ECU that you've lifted off the throttle and anything over 2kRPM's - this is a guarantee range where the stock ECU should cut all fuel off at the fuel injectors.
With a TPS that's not "zero'd out", the stock ECU still thinks you're (slightly) on the throttle, thus still trying to inject fuel into the engine...
Cycling idle is a sign of an intake leak...
With increased air (due to leak) getting into the engine, it starts to nudge the RPM's higher, since idle is usually on the rich side anyways.
It hits around 1,800RPM where the stock ECU sees that the TPS is supposedly adjusted "closed" and goes WHOA - this is decel fuel-cut territory, so it cuts the fuel off.
Endless cycle...
Now, I realize that these two conditions are mutually exclusive.
At this point, you've eliminated the bottom condition, but you still got the top one - the misadjusted / bad TPS.
Did you test resistance of your TPS yet?
I don't think your condition is exclusive to the exhaust leak...
It could be, but that's a long shot- usually stock ECU doesn't care what happens after the exhaust exits the engine.
(Well, not true if we're talking about the O2 sensor, but the O2 sensor is ignored at idle.)
Stock electronics SUCK donkey balls; that's why I yanked that sh*t years ago and installed my Haltech E8.
-Ted