You forgot the most critical piece of gear IMO. You need a signaling device. With a good signal device, you may not need the other gear.
My last piece of essential gear that I bought was a pack orange smoke flares. Looks like they are considered a nautical device, but I bought them with an inland situation in mind. My inspiration came from a trip to the desert this fall, where some hikers apparently thought it would be a good idea to head all the way up the mountain trail on a 109 degree day with very few places to get shelter from the sun. There was a chopper circling around up there trying to spot them (I'm guessing they had called in from a cell phone). I would imagine that they would have paid whatever the asking price was for one smoke flare at that point. Of course fire and signal mirrors can also be used, but if you are barely holding on out there (which very well may have been the case given the brutal sun), popping a flare may be all you can muster. Obviously a whistle or something like a small airgun would be great for when the ground crew is coming your way.
For a rainy forest, the sound devices would still be great if rescuers are relatively close on the ground, but this post got me thinking about picking up some sort of signal flares that can get above the canopy.
The next essential that came to mind would be a satellite phone or some other reliable mode of communication when you are in a remote area (i.e. where you most need communication). Unless you are in an area where help just isn't going to get to you no matter what, I think that is going to be about as essential as you can get if you find yourself in the WORST kind of pickle (e.g. bad injuries and/or stuck in elements that are going to beat you down very quickly).
Another thing that came to mind was, of course, an ample supply of water, AND electrolytes/vitamins. That sun will suck both out of you in no time, and if you lose either one of these things, you are pretty useless to do anything. I guess in the rainy scenario, protection from the wet/cold takes the place of these concerns, and so I second the notion of some good rain gear and a tarp. And fire making tools.
The other essential tool that always come to mind for me is a first aid kit. I'm still working through what are the real essentials of survival first aid, but I think a good lightweight splint, protection against blood loss (celox, tournequit, field dressing), some treatment for bad burns, some surgical tools/latex gloves, and a few basic drugs (anti-inflamatory, anti-histamine, trip anti-biotic/iodine, etc.) are among them.
also good chopper and slicer)