It's been a while (and, I don't feel like wallking thru the rain to the garage, pulling the cover off, and playing with it again...), but...
Pop the bulb carrier off (you've got that far.)
The reflector is held in by a snap-tab or two on each end (?) - should just need a small flat-head screwdriver to release it.
I don't remember if the housing is bonded to the glass, or secured with spring tabs. Some little corner of my mind, though, says that it was bonded.
Anyhoo, once the reflector & lens are out, the hole is big enough to reach thru & clean things.
how to fix the lens:
once the back cover is removed you can feel the reflective housing where the bulbs go into
this removes by pulling on it it. i grabbed and kind rotated it down and it popped out
with this i was able to put the red lens back on in the pic below you can see the tabs holding this in place
on the sides i noticed i could stick my fingers into a hole pic below
looks like there is a tab or some sort of piece to hold the cover on. I might be completely wrong
There are two metal mounting tabs glued to the glass. You can see them in the above pic but can't see them from the outside of the car, due to the black paint on the glass. The entire brake light assembly slides onto the tabs and clips into place. I'm almost positive that it slides on from the top. You can pry gently on the plastic tabs and slide the assembly off of the clips.