Pax Klanq, I Presume?
With Grit Gate secured, we finally meet the enigmatic leader of the Barathrumites, 
Barathrum himself. In order to further the goals of the enclave, he has tasked us with securing the assistance of a fungi who owes a favor. Live and drink, disciple.
Recommended
| Level | Abilities | Stats |
|---|---|---|
| 30 | Perfect  Flight, -249+ Ooze reputation, -249+ fungus reputation or  love injectors, 125 quickness, 200 movement speed | 8  AV and 20  DV or 15 AV |
The First Riddle
This quest is an interesting one; as depending on your knowledge it can be extremely dangerous or one of the safest quests in the game. The quest involves you solving a few riddles that are always the same and talking to 
Pax Klanq at the end of it all. Before setting out on your journey, it is critical that you either have neutral (-249 and above) reputation with fungi or a love injector or two; as Pax Klanq himself is a member of the fungi faction and will be hostile to you otherwise. Since you start off neutral to fungi, this basically just means don't mess up that relationship. If you do, the easiest way of gaining rep is to gain a fungal infection or two.
The first part of the quest is to go to the center of the Rainbow Wood. This is most easily done from the direct north or south of the Rainbow Wood. Traveling on the world map onto a Rainbow Wood tile will immediately cause you to get lost, and you will be dropped in a random zone in that parsang. This is bad since it can easily cause us to miss our mark. Instead, once you get to the edge, drop into the Jungle and just go north/south to the center.
The High Life
Once you get to the center, you'll receive a popup telling you that you completed the quest step and you'll know you're in the right place. Here, you'll find elcatl plants that can be 
Harvested for Eater's Flesh. If you don't have the 
Harvestry skill, you can find a corpse here with a kelp scroll, a credit wedge and some Eater's Flesh. You then need to eat the Eater's Flesh and follow the orange colored brick path that appears all the way to Pax Klanq's hut.
🗒️ Note: You cannot see
Once you arrive at the hut, break down the walls and talk to Pax Klanq. Let them puff on you and turn in the quest to Barathrum. You'll of course still be infected with 
Klanq, but the requirements of this quest are rarely something difficult at this point in the game. Some will test your memory and/or your game knowledge in order to find, as they can be rather obscure.
Sludges
Now, we have not addressed the elephant in the room, which is the 
soupy sludge that contaminates the Rainbow Wood. These are members of the ooze faction and are the only enemy you will find here (normally; legendary creatures like mechanimists and templar can be found here rarely). So if you are at least neutral with them, you're home free on this quest. This is the route I would advise, as ooze rep is not only fantastic for this quest, but for the rest of the game as well. High level oozes are very powerful, so it's better just to avoid them.
Unfortunately, this solution is somewhat just down to chance. If you're unlucky in finding legendaries to ritual/kill for ooze rep, or can't find any applicable Schrodinger pages, we'll need another solution. As far as getting to the center goes, we'll be moving through the zones fast enough that we'll be on to the next before any soupy sludge can form. However, for every zone after we eat the Eater's Flesh, we will have a heavy hit to our quickness (-60). Monosludges will be incapable of catching up with us, so with a little boost to our quickness or move speed (or better yet, both), we'll be fairly safe in moving through the zones. The recommended levels are higher than you'll probably need, but offer enhanced safety.
The second best solution, however, is perfect Flight. This is attainable through either 
anti-gravity boots or level 6 
Wings (or cathedrae, for an overpowered solution). The soupy sludge have no way to hit a flying target, so we can walk through on our own time. The only downside to this solution is that Pax Klanq themself will attempt to kill the sludges, so ideally you can pair this with some 
Phasing (ideally you can cook with phase silk just before eating the Eater's Flesh). If Pax Klanq ends up dying, just wait around for 500 turns or so for them to come back.
The shimmering effect causes quite the debuff of -60 quickness, so if you don't have any of the solutions you can get by with either enhanced quickness or enhanced movespeed (especially with 
Multiple Legs). A monosludge doesn't have much quickness to speak of, but the more liquids it can consume the faster it will move so don't wait around for it to power up.
The soupy sludge will nearly endlessly form, so it's not worth fighting any of them when encountered. Simply focus on the path ahead and ignore them until you can get to Pax Klanq.