Seafoam sells a kit with a special hose that fits between the intake duct and the throttle body. You just loosen the duct clamp and slip the hose in, start the engine and start the spray. Takes about 6 or 7 minutes, then you have to shut down for a specified time, remove the hose and tighten the clamp and then do a couple of minutes of “spirited” driving to finish the procedure.
Edit: when warmed up, take some kind of spray such as WD-40 or carb cleaner and spray arond the #1 intake port top front to see if the idle is affected. If it is, then intake gasket is leaking causing your #1 to run lean and #4 to run rich with 2 and 3 in between. That would carbon up #4 and maybe #3 as well.
Edit #2: you do not need to remove the intake manifold, just the EGR. It has been awhile since I had a Saturn but I did have to do that on mine. It was one of the very few issues I had with the vehicle, took mine to 275k before selling it.
Edit #3: Looking at your picture, I may not be remembering correctly. I had to remove the EGR valve to clean it now that I think of it, both ports, the intake and exhaust were right under it, but I had to clean out both of them.
The port I had to clean on the exhaust manifold was for the Air Injecting Reactor (AIR). I was getting a code for the AIR not working which indicated that the air pump was not working. AIR is supplied the first two minutes after a cold engine is started to get the catalytic converters to start working. The PCM does not actually monitor the pump but the cats instead, If it doesn’t see them working, which they won’t without the additional air because the FI is injecting extra fuel, it sets the code. The pump was working just fine, the reed valve between the AIR and the manifold was not iced up (most common cause for this code). Found the clog inside the port of the manifold. BTW that port is cast in and about 2" long.
You can see on your picture there that the #1 intake port is not supported at the top front because of the power steering pump doesn’t allow for a bolt there. That is where the fabric gaskets would get sucked in. I got a metal backed gasket the second time mine failed.