There is another point that might not be obvious to people that played Deep Dungeons when they were new: To get into Heavens on High and Eureka Orthos, you need to have finished level 50 of Palace of the Dead. I tried this once (when it was part of a Moogle event), and failed miserably. The groups I got into weren't able to do it, and when I tried it solo, my weapon and armor level were way to low, I got stuck somewhere in the 30-40 range.
At this point I lost interest, so I will never be able to enter any of the other Deep Dungeons.