Wooow.. Now that sounds like an incredible cool dream right there!!

I've planned to visit my subconscious for a long time now, but I haven't got the chance yet.. What I have pictured myself doesn't come close to what you've described there!! When I get the chance to attain a high level of lucidity and come up with the idea to pay my subconscious a little visit and show who's boss, it will be in a large building. Maybe a person will act as a guide there, maybe not. What's certain, is the fact that there will be an enormous control room with a large variety of buttons and monitors where I can see the current status of my subconscious and where I will be able to adjust all the settings to enhance lucidity and mindfulness and the level of my concentration!

About the checkerboard and the roman numerals.. I have no clue what it could mean. It appears that it's counting downwards, except for the top left one.. Maybe the next time when you get the chance to visit the same place, you could go sit in front of the checkerboard and play a game with your subconscious!!