Was pretty much already answered, but just for a little clarification:
Monster levels are not all the same, so there is some variation below and above your character level. When you are solo this should be a subtle variation, but when you are in a group, the variation should be a bit higher. Either way, you'll start to see the first level 55s dropping (usually from EPs since normal mobs tend to drop higher tiers infrequently) at level 63 (driver level), but this doesn't mean all the EPs you are fighting have a chance to drop level 55s, so if you want more of the EPs to have a chance at dropping level 55s, you'll want to level up to around 65ish. From my experience it doesn't actually increase your odds of getting level 55s by leveling a lot more, even though theoretically it should cause all mobs to have a chance of dropping level 55s. If you'd like my speculation on why that is, feel free to PM me.
If you are down a trapdoor, the mobs will gain +1 - 5 levels (per trapdoor) and so consequently you will have a chance to get level 55 drops from these monsters at a lower level. So with a +5 level trapdoor and a level 58 driver, it is already possible to get level 55s. It is also possible to be, as an example, level 52 and go down 4 trapdoors (+1, +4, +3, +2) and get level 55s to drop. Note that although your level will be lower, killing EPs down that many trapdoors will be a lot harder than if you were level 65, so don't think of it as an easier route for obtaining endgame drops.
As an aside, monster difficulty does not increase the max tier of drops from my testing. So running a +% monster difficulty map at a lower level will not produce higher level drops.
Hope this helps... and also hope it wasn't too much info