Elantra XD (2001-06) :: RPMs Occasionally Bounce Persistently Below 3000

I've got an automatic transmission 2002 elantra 2.0 that I purchased in 2009. About a year after owning it a weird problem developed that I've just sort of lived with since. Between 25-40 mph my RPMs occasionally "bounce" persistently by an amount between 500 (mild) and about 1000 (severe). There's a bit of fluctuation insofar as what RPMs/speeds it happens at depending on outside temperature and how warm the engine is (higher temps correlate with this issue happening at higher RPMs and a more pronounced fluctuation), but it's a consistent issue every time I drive. It *seems* like my car is always trying to push down the revs, hits a certain low point depending on the gear/speed, then jumps up just a bit only to edge back down. Lather, rinse, repeat. It's not simply a display problem as I can feel and hear the engine revs changing.

No fluctuations at idle. Above 3000 RPMs it's ALWAYS smooth sailing. When I'm actively accelerating there's never a problem, even if my acceleration stays in the revolution problem range. The car is never in danger of dying, but if the cruise is engaged (ESPECIALLY in the 25-30 MPH range at operating temp) the car shudders uphill - I assume this is because the RPMs dip a bit too low for the gear the car is in. If I press the throttle the car responds normally. This bouncing RPM issue itself NEVER causes the car to shift gears in response, and if it's happening and the car DOES shift everything works fine until it goes back to trying to maintain RPMs in the problem range. When it happens I usually just increase speed by 5MPH and it goes away, though if the car is warm and the speed limit doesn't allow me to go fast enough to get out of the problem range it just does the same thing at the slightly higher RPMs.

When the problem started my car threw an OBD code - I didn't read it myself and brought the car to a random service shop who SAID they changed the throttle position sensor, and the code was gone, but a few days later it was doing the same thing without throwing a code. I tried changing the fuel pump thinking it was a fuel delivery problem, but that didn't solve anything. I put seafoam in the fuel system monthly so I'm fairly certain that fuel system gunk isn't an issue. The symptoms haven't changed AT ALL during the 6+ years this has been happening.

The kicker is that a few years ago I found a SUPERB mechanic - the first one I've ever actually trusted to be not only competent but also honest. Described the problem and even demonstrated it to him. When I brought in my car to have the struts and mounts replaced he spent two days trying to figure out what was causing the RPM issue too... and couldn't nail it down.

Possibly related: after starting the car - regardless of how long it's been running - there's a brief delay between pressing the gas pedal and the engine responding. Delay seems *slightly* longer the colder it is outside, but it's never more than a second and a half. No further delays unless I shut the engine off and turn it on again. Replacing the fuel pump didn't affect this matter whatsoever.