You say there's a difference wet or dry. Do you mean rain, not rain, high humidity or not? Could it really maybe be a temperature difference?
Does it start OK all the time?
Like has been mentioned, timing chain is OK? Most people find the 125,000 interval the max the chain will go. It could be stretched and not failed, which will throw the idle off.
Rough idle on a 22R-E is usually one of a few things. Check vacuum lines first. Any dependency to the brakes being pushed or not?
The Aux Air Valve (or sometimes called the Idle Air Control) is often the issue with bad idle on a 22R-E. This is the coolant controlled valve on the bottom of the throttle body. Expensive sucker, about $150, but available at Auto Zone, NAPA, Toyota dealer and so you can shop around. I would verify that your EFI temp sender is right, if that's gone wonky it throws the ECU for a loop. Also the O2 sensor might be going out. Beyond that, the Cold Start Injector, if it's leaking, will make it idle poorly. Also the EGR valve or vacuum modulator can stick and that throws the idle off.
Might just be time to take the intake apart and clean all the black goop from inside it. If you pull off your intake hose from the front of the throttle body and hold the butterfly open it will probably look like a black hole. The inside of the intake plenum and intake runners get coated in this mixture of unburned gas, oil from the PCV and soot from the EGR. It's nasty and most people find a much better throttle response when they just clean that and the throttle body.